Question

A population of 400 beetles grows by 5% each week. How can the beetle population be determined after a number of weeks, w?

Answer 1

*5% in decimal form is 0.05.

After one week we have:
N=400*1.05 beetles

After two weeks we have:
N=(400*1.05)*1.05 beetles

After three weeks we have:
N=((400*1.05)*1.05)*1.05 beetles

We can write this as:
Week 1:
$N=400* 1.05^{1}$
Week 2:
$N=400* 1.05^{2}$
Week 3:
$N=400* 1.05^{3}$

From this we can make conclusion that formula for number of beetles after w weeks is given by:
$N=400* 1.05^{w}$