Question

A wildlife biologist determines that there are approximately 200 deer in a region of a national park. The population grows at a rate of 7% per year. What is an exponential function that models the expected population?

A. f(x) = 200(0.07)x
B. f(x) = 200(1.07)x
C. f(x) = 1.07(200)x
D. f(x) = 7(200)x

Answer 1

Answer:

Option B.

Step-by-step explanation:

A wildlife biologist determines that

Initial population of deer = 200

Growth Rate = 7% = 0.07

The general exponential growth function is

$f(x)=a(1+r)^x$

where, a is initial value, r is growth rate and x is number of years.

Substitute a=200 and r=0.07 in the above function.

$f(x)=200(1+0.07)^x$

$f(x)=200(1.07)^x$

The exponential function that models the expected population is $f(x)=200(1.07)^x$.

Therefore, the correct option is B.

Answer 2

The exponential function that models the expected population of deer in the region of national park is  

$\rm \bold{f(x) = 200(1.07)^x }$

hence option (B) is correct

Given

A wildlife biologist determines that there are approximately 200 deer in a region of a national park.

The population grows at a rate of 7% per year.

We have to determine is an exponential function that models the expected population.

The general exponential function is given by the  equation (1)

$\rm f(x) = a(1+ r)^x..........(1) \\Where \; \\ a = Initial \; Value\\r = Yearly \;Growth\; Rate \\x= Number \; of \; years$

Initial number of deer = a = 200

r = Yearly growth rate = 7%

On putting  the values in equation (1) we get

$\rm f(x) = 200(1+ 0.07)^x \\\bold{f(x) = 200(1.07)^x }$

So the exponential function that models the expected population of deer in the region of national park is  

$\rm \bold{f(x) = 200(1.07)^x }$

hence option (B) is correct.

For more information please refer to the link below

https://brainly.com/question/11487261