Question 884547
in 2000, the population of the united states was 286.75 million and the exponential growth rate was 1.3% per year

a) Find the exponential growth function.
b) Predict the U.S. population in 2005.
C) when will the world population be 8.0 billion?

Formula I think to use: P(t) = {{{P0e ^rt}}} yes, you are correct.
.
a) Find the exponential growth function.
A(t) = {{{286.75e^(.013t)}}}
b) Predict the U.S. population in 2005.
t = 2005-2000 = 5
A(t) = {{{286.75e^(.013t)}}}
A(5) = {{{286.75e^(.013*5)}}}
A(5) = {{{286.75e^0.065}}}
A(5) = {{{286.75*1.0672}}}
A(5) = 306.008 million


C) when will the world population be 8.0 billion?
set A(t) to 8 billion and solve for t
A(t) = {{{286.75e^(.013t)}}}
8000 = {{{286.75e^(.013t)}}}
8000 = {{{286.75e^(.013t)}}}
27.8988666085 = {{{e^(.013t)}}}
ln(27.8988666085) = .013t
ln(27.8988666085)/.013 = t
3.32858606465/.013 = t
256.045081896 = t
or approx
256 = t
2000 + 256 = 2256 (the year)