Question

A study is done on the population of a certain fish species in a lake. Suppose that the population size P(t) after t years is given by the following exponential function. P(t)=280(1.29)^t

Find the initial population size?
does the function represent growth or decay?
By what percentage does the population change each year?

Answer 1

280

function represent growth.

29 %

Answer 2

1. 280
2. function represent growth.
3. 29 %

Explanation:

Equation to calculate population size after time, t

P(t) = 280(1.29)^t

To find initial population size we will take t = 0

P(0) = 280(1.29)^0

= 280(1)

= 280

To find that function represent growth or decay

P(1) = 280(1.29)^1

= 280(1.29)

= 361.2

Its means that after a year population increases. Hence, function represent growth.

By what percentage does the population change each year?

(361.2 - 280 / 280) * 100%

= 29 %