Question

Is my answer correct?

Answer 1

Here is the answer to the given problem above. 
Here is the exponential function to model this situation:
f(x) = 420(0.79)x
Now, solve with the given values.
P(t)=420×(.79)^t P(5)=420×(.79)^5=129
So the answer would be 129 animals.
Hope this answer helps. Thanks for posting your question!

Answer 2

Answer:

$y=420\cdot (0.79)^x$

The value of the function after 5 years would be 129.

Step-by-step explanation:

We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.

We know that an exponential function is in form $y=a\cdot b^x$, where,

a = Initial value,

b = For decay b is in form $1-r$, where, r represents decay rate in decimal form.

$r=21\%=\frac{21}{100}=0.21$

$y=a\cdot (1-r)^x$

$y=420\cdot (1-0.21)^x$

$y=420\cdot (0.79)^x$

Therefore, our required function would be $y=420\cdot (0.79)^x$.

To find the value of the function after 5 years, we will substitute $x=5$ in our function.

$y=420\cdot (0.79)^5$

$y=420\cdot 0.3077056399$

$y=129.236368758$

$y\approx 129$

Therefore, the value of the function after 5 years would be 129.