Question

A species of beetles population grows 32% every year. suppose 100 beetles are released into the field. construct an exponential model for this population.

Answer 1

The correct answer is: $100*(1.32)^x$

Explanation:

The exponential form should be like: $ab^x$

Where a = 100
b = 1.0 + 32/100 = 1.32 (since 32% growth every year)
x = Years

Therefore the form would becomes:
$100*(1.32)^x$

Let's verify this form:

After 1 year; x = 1:
$100*(1.32)^1$ = 132 (As expected since there is 32% increase every year; Hence 100 + 32 = 132)

After 2 years; x = 2:
$100*(1.32)^2$ = 174.24 ((As expected since there is 32% increase every year; Hence in first year:100 + 32 = 132 whereas 32% increase of 132 would be 42.24; hence in second year: 132 + 42.24 = 174.24) and so on... (verified)