An exponential function can either represent population growth or population decay
How to model the populationThe question is incomplete, as the resources to model the population of the Western Lowland Gorillas are not given.
However, the following is a general guide to solve the question.
An exponential function is represented as:
[tex]y=a(1 \pm r)^x[/tex]
Where:
(a) represent the initial value i.e. the initial population of the Western Lowland Gorillas (r) represents the rate at which the population increases or decreases.(x) represents the number of years since 2022(y) represents the population in x yearsGiven that the population of the Western Lowland Gorillas decreases, then the rate of the function would be 1 -r (i.e. an exponential decay)
Take for instance:
[tex]y = 20000 * 0.98^x[/tex]
By comparison.
a = 2000 and 1 - r = 0.98
The above function can be used to model the population of the Western Lowland Gorillas
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The steps to integrate this problem using trigonometric substitution.
Answer:
[tex]I=\frac{x^3}{3(25x^2+1)^{3/2}}[/tex]
Step-by-step explanation:
(a)
[tex]5x=tan{\theta}\\x = \frac{\tan{\theta}}{5}\\dx=\frac{1}{5}\sec^2{\theta}d\theta\\[/tex]
[tex]I=\frac{1}{125}\int\frac{tan^2{\theta}sec^2{\theta}}{(tan^2{\theta}+1)^{5/2}}d\theta[/tex]
[tex]I=\frac{1}{125}\int\frac{tan^2{\theta}sec^2{\theta}}{sec^5{\theta}}d\theta[/tex]
[tex]I=\frac{1}{125}\int\frac{tan^2{\theta}}{sec^3{\theta}}d\theta[/tex]
[tex]I=\frac{1}{125}\int\sin^2{\theta}{cos{\theta}}d\theta[/tex]
[tex]I=\frac{1}{125}\int\sin^2{\theta}d\sin{\theta}[/tex]
[tex]I=\frac{1}{125}\frac{1}{3}sin^3{\theta}}[/tex]
[tex]I=\frac{1}{125}\frac{1}{3}(\frac{5x}{\sqrt{25x^2+1})})^3[/tex]
The Recreation CPI index number was 93.0 in 1994 and 95.6 in 1995. What was the
percent increase in the prices of recreation goods and services for 1995, to the nearest tenth percentage?
Answer:
2.7957
Step-by-step explanation:
To calculate percentage increase we- the final value by the starting value so in 1994 we have 93 and in 1995 we have 95.6.
95.6 - 93 = 2.6
We then divide 2.6 by the absolute value of value 1(93) so 2.6 divided by 93=0.02795698924
Then use a calculator if you would like you don't have to but times that answer 0.02795698924 by 100. and you get the percent increase.
0.02795698924 x 100=2.7957.
Hope it helps have a great day:)
The wind speed near the center of a tornado is represented by the equation S=93logd+65, where d is the distance, in miles, that the tornado travels and S is the wind speed, in miles per hour.
If the wind speed was 150 miles per hour, how many miles did the tornado travel? Round your answer to the nearest tenth.
Step-by-step explanation:
please, be careful when writing the problem definition.
the formula is as I understand it from the definition
S = 93×log(d) + 65
with log being truly the logarithm to the base 10.
so, we have
150 = 93×log(d) + 65
85 = 93×log(d)
log(d) = 85/93
d = 10^(85/93) = 10^(0.913978495...) =
= 8.203109232... ≈ 8.2 miles
the tornado had traveled 8.2 miles.
The required tornado traveled about 8.2 miles to achieve a wind speed of 150 miles per hour.
To find the distance (d) that the tornado traveled when the wind speed (S) was 150 miles per hour, we need to solve the given equation for d.
The equation representing the relationship between wind speed (S) and distance (d) is:
S = 93 * log(d) + 65
We are given that S = 150, so we can substitute this value into the equation:
150 = 93 * log(d) + 65
Now, let's solve for log(d):
93 * log(d) = 150 - 65
93 * log(d) = 85
Now, divide both sides by 93:
log(d) = 85 / 93
Next, find the antilog of both sides to solve for d:
[tex]d = 10^{85 / 93}[/tex]
Using a calculator, we get:
[tex]d = 10^{0.91397849462}[/tex]
≈ 8.2
Rounded to the nearest tenth, the tornado traveled approximately 8.2 miles.
So, the tornado traveled about 8.2 miles to achieve a wind speed of 150 miles per hour.
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PLEASE HELP!! Multiple Choice 1. Calculate the slant height for the given cone. Round to the nearest tenth (11 Diameter = 8 cm Height = 9 cm O 10.2 cm O 11.4 cm 09.8 cm O 12.0 cm
==============================================
Explanation:
Refer to the figure below.
The cone has a circle at the base which has a diameter of 8 cm. This cuts in half to 4 cm, and that's the radius. This forms the horizontal leg of the right triangle highlighted in red.
The vertical leg of the triangle is the height of the cone (9 cm).
---------
Use the pythagorean theorem to find the hypotenuse of the triangle, which is exactly the slant height.
a^2 + b^2 = c^2
4^2 + 9^2 = c^2
16 + 81 = c^2
97 = c^2
c^2 = 97
c = sqrt(97)
c = 9.84886
When rounding to one decimal place, we get 9.8 cm which is the final answer.
f(x)= 5x+7
g(x) =3x-1
find: f(g(x))
Answer: 15x+2
Step-by-step explanation:
f(g(x))=f(3x-1)=5(3x-1)+7=15x-5+7=15x+2
A certain region of America with over 500,000 households has a mean household income of $70,000 with a standard deviation of $20,000. Economists plan to take random samples of 625 households and calculate the sample mean income -x for each sample.
Calculate the mean and standard deviation of the sampling distribution of -x.
The mean and the standard deviation of the sampling distribution of x are given as follows:
Mean: $70,000.Standard deviation: $800.How to obtain the mean and the standard deviation?The mean and the standard deviation of the sampling distribution of x are obtained using the Central Limit Theorem.
The mean is the same as the population mean, hence it is given as follows:
$70,000.
The standard deviation is given by the population standard deviation divided by the square root of the sample size, hence:
20000/25 = $800.
(as 25 is the square root of 625).
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Please find the average of 9,12, 7, 11 and 8
No messing
Answer:
9.4
Step-by-step explanation:
Average = Sum of all values/ Total number of value
= 9 + 12 + 7 + 11 + 8/ 5 (as there are 5 numbers, which are 9, 12, 7, 11 and 8)
= 47/5 = 9.4
So the average is 9.4
Hope you understood!!
Aswer: 5x - 2 = 3x + 4
Answer:
x = 3
Step-by-step explanation:
5x - 2 = 3x + 4
2x = 6
x = 3
round 5.1249 to the nearest tenth
Answer:
5.1
Step-by-step explanation:
The tenth's place is the first digit after the decimal. For rounding if the number behind your specific place is greater than or equal to 5, you round it up one number, if it is below 5 the number stays the same.
Example:
If I want to round 6.68 to the tenth's place since the 8 is greater than five, my 6 goes up one number and we get rid of the other numbers. Therefore it would be 6.7
If I want to round 6.64 to the tenth's place since the number is not greater than or equal to five, the number stays the same and we get rid of the others. Therefore it would be 6.6
In your case of 5.1249, we only look at the number after the tenth's place to check if it is greater than or equal to five, which it is not, which is why we do not round up, giving us 5.1.
Answer:
5.1
Step-by-step explanation:
5.12
5 is in the whole number place
1 is in the tens and 2 in the hundredths place
which table is a linear function A. input 2,5,9,11 output 7,16,28,34 B. input1,2,3,7 out put 1,4,16,49 C. input 2,4,5,16 output 1,13,22,33 D. input 1,2,4,7 output 2,10,26,65
Answer:
bro im on the same question u on we might as well guess u know
Step-by-step explanation: no
A number is increased by 5% twice. This can also be written as" a number is increased by __% (see attachment below)
Answer:
a number is increased by 5%
Next time, the rabbit from the previous problem start at 10 where on the number line can he be after the same three jumps?
Previous problem : A rabbit started at point 0 and made 3 jumps: a jump of 4 units, then a jump of 2 units, and then a jump of 1 unit. We do not know the direction of either jump. Where on the number line can this rabbit be now?
the answers to the first problem are: -7, -5, -3, -1, 1, 5 and 7
Answer:
-2 tried my best hope I get it
A cars velocity on a straight highway increases uniformly from 20km/h to 70km/h in 0.008h. Find the acceleration in km/h2
Answer:
a = 70 km/h - 20 km/h / 0.008 h = 50 km/h / 0.008 h = 6250 km/h²
acceleration is change in velocity over time
acceleration = (final velocity – initial velocity) / Time
= (70km/h – 20km/h) / 0.008h
= 6250 km/h²
mark as brainliest plis
Write the polynomial function in standard form when given the leading coefficient and the zeros of the function?
Leading Coefficient: 2
Zeros: 6, -2, 2
How does f(x)=2x3^x change over the interval form x=5 to x=6
Answer:
I realise you've probably gotten past this question, but I'm throwing it out for all future askers of this question ¯\_(ツ)_/¯
C) ƒ(x) increases by a factor of 3
ƒ(x) increases by a factor of 3
f(4) = 3^4
f(5) = 3^5
f(5) /f(4) = 3^5 /3^4 = 3^5−4 = 3^1 = 3
The value of ƒ(x) changes from 81 to 243 over the interval from x = 4 to x = 5.
This is an increase by a factor of 3.
Step-by-step explanation:
1 pts
Which expressions are equivalent to 100? Select all that
apply.
Answer:
where is the pictures??
please somebody help me w it this .
Answer:
So you need to find the surface area...
Step-by-step explanation:
The length is 20, the width is 14, and the height is 10. It is a rectangular prism so it has six sides.
Two of the sides are l*w
Two of the sides are w*h
and two of the sides are l*h
This gives us equations of 2*(20*14), 2*(14*10), and 2*(20*10)
simplify that to 2*280, 2*140, and 2*200. Then you simplify that to,
560,280,and 400. Now simply add these numbers together to get.
1240.
So your answer is...
ANSWER: 1240 cubic units
Bob tied the end of his kite to a stake in the ground 1tft away from a 14ft tall street light. The top of
the kite touches the top of the street light. If the body of the kite is 4ft, how long is the kite string?
A.) 19. 1ft
C.) 13.8ft
B.)17 8ft
D.) 21.8ft
what are corresponding angles
Answer:
Corresponding angles are equal. They're a F shape and it could be upside down.
Write the expression 12 × 4-2( the 2 is for the symbol squared.) in words.
WILL GIVE BRAINLY!!!!! :)
Answer: Twelve times four squared
Step-by-step explanation: hope it helps
which figure has a shaded area equal to the fraction 1/2 ?
Answer:
a circle because slit it in half.or actuall any shape
anyone know the answer?? the question is the sreenshot
Answer and solution in the picture hope it helps
Mark has a coupon for 10% off his entire purchase. If Mark buys $41.00 worth of merchandise, how much will Mark spend? *
Answer:
36.90
Step-by-step explanation:
41 X 0.10 = 4.10
41 - 4.10 = 36.90
H weill spend 36.90 dollars.
Please mark brainliest!
Have a great day!
Answer:
90 cause u take 10% off
Still, stuck? Get 1-on-1 help from an expert tutor now.
:
. The population of a city decreased from 25,000 to 24,000. Find the decrease percentage. at to be paid
Answer:
4%
Step-by-step explanation:
1000 of 25000 is 4%
3p+85
12p - 10
P=?
Please help I have school in like 5 minutes I’m super desperate
Answer:
1013p
Step-by-step explanation:
3p + 85 . 12p - 10p
3 + 85 ⋅ 12−10
3p +85⋅12p−10p3+1020−10 in all equals 1013p!
A drink is made from orange juice and lemonade in the ratio 3 : 7. How much lemonade is needed if 60 ml of orange juice is used?
A. 110 ml
B. 120 ml
C. 130 ml
D. 140 ml
Answer:
140 ml
Step-by-step explanation:
60/3 = 20
20x7 = 140
PLEASE HELP FAST ILL GIVE BRAINLIEST The volume of 1 can of Pepsi is 0.4
liters. What is the volume of 10 cans?
.
O A. 0.004 liters
DB.
B. 4.0 liters
O C.40.0 liters
O D. 0.04 liters
Answer:
B. 4.0 liters
Step-by-step explanation:
1 can = 0.4 l
10 cans = 0.4l x 10
0.4l x 10 = 4l
10 cans = 4l
The area of a rectangular field is 7050 m2.
If the width of the field is 75 m, what is its length?
Answer:
l = 94 m
Step-by-step explanation:
The formula for the area of a rectangle is l*w where l is length and w is width. We know that the width is 75 and the area is 7050:
7050 = 75*l. get l by itself by dividing both sides by 75
l = 94 m
g(n) = (n + 2)²
g(n) = ?
»g(n) = (n + 2)²
»g(n) = (n + 2)(n + 2)
»g(n) = n(n + 2) + 2(n + 2)
»g(n) = n² + 2n + 2n + 4
»g(n) = n² + 4n + 4✅
Answer:
g'(n) = 2(n + 2)
Step-by-step explanation:
g(n) = (n + 2)²
g(n) = n² + 4n
g'(n) = 2n + 4
g'(n) = 2(n + 2)
Help please please please
Answer: I think that the answer is 1,944 I think
Step-by-step explanation: 216 x 3 = 1,944
