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?

280 function represent growth. 29 %

Step-by-step 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 %