Question

There is a pond on my property that Wildlife and Fisheries stocks. From information provided to me, I can expect my fish population to be
200 * 2^t/4 after t years.
a. How many fish were stocked in my pond initially?
b. What is the growth factor? The growth rate?
c. How many fish are in my pond after 5 years?

Answer 1

An exponential function can either represent growth or decay

• The initial value is 200 and the growth factor is 1.190
• The number of fish in the pond after 5 years is 436

(a) The initial number of fish and the growth factor

The function is given as:

$P(t) = 200 \times 2^{t/4}$

An exponential function is represented as:

$P(t) = ab^t$

Where

• a represents the initial value
• b represents the growth factor

So, by comparison: the initial value is 200

The growth factor is then calculated as:

$b = 2^{1/4}$

$b = 1.190$

Hence, the initial value is 200 and the growth factor is 1.190

(b) The number of fish after 5 years

This means that t = 5.

So, we have:

$P(t) = 200 \times 2^{t/4}$

$P(5) = 200 \times 2^{5/4}$

$P(5) = 200 \times 2^{1.125}$

$P(5) = 436$

Hence, the number of fish in the pond after 5 years is 436

Read more about exponential functions at:

brainly.com/question/11464095