Question

The number of animals in a population is 775, and it increases by of 51% each year.

Answer 1

Answer(a):

Exponential growth formula is given by

$A=P(1+r)^t$

Where preset population = P= 775

Rate of increase = r = 51% = 0.51

t= number of years

A= Future value.

Plug these values into above formula:

$A=775(1+0.51)^t$

$A=775(1.51)^t$

Hence required exponential function is $A=775(1.51)^t$

Answer(b):

plug t=10 years

$A=775(1.51)^t=775(1.51)^{10}=775(61.6267795034)=47760.7541151$

which is approx 47761.

Answer(c):

Plug A=1150

$1150=775(1.51)^t$

$\frac{1150}{775}=(1.51)^t$

$\ln(\frac{1150}{775})=t*\ln(1.51)$

$0.394654192004=t*0.412109650827$

0.957643654334=t

Which is approx 1 year.