Answer :
A general exponential model can be described by:
[tex]P(x)=A\cdot b^x[/tex]Where A is the initial condition, and b is the growth factor. From the problem, P is the population (in millions); if x is the number of years passed since 2011, then x = 0 in 2011:
[tex]105=A\cdot b^0\Rightarrow A=105[/tex]We know that the growth rate is -0.657% = -0.00657. The growth rate r and the growth factor b are related by:
[tex]b=1+r\Rightarrow b=1+0.00657=0.99343[/tex]Our model is now complete:
[tex]P(x)=105\cdot0.99343^x[/tex]For the year 2024, x = 13 years have passed. Then, we calculate the population using our model (rounding to the nearest hundredth):
[tex]P(x=13)=105\cdot0.99343^{13}=96.38[/tex]The size of the population in 2024 will be about 96.38 million
