SOLUTION: Can someone please show me the steps on how to solve the following problem? Section 12.4; #99 Directions: The formula A=36.1e^0.0126t models the population of California, A,

Question 364471: Can someone please show me the steps on how to solve the following problem?
Section 12.4; #99
Directions: The formula A=36.1e^0.0126t models the population of California, A, in millions, t years after 2005.
a.) What was the population of California in 2005?
b.) When will the population of California reach 40 million?

Any help is appreciated.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Directions: The formula A=36.1e^0.0126t models the population of California, A, in millions, t years after 2005.
a.) What was the population of California in 2005?
t=0
subsitute into:
A=36.1e^0.0126t
A=36.1e^0.0126(0)
A=36.1e^0
A=36.1 million
b.) When will the population of California reach 40 million?
A = 40
subsitute into:
A=36.1e^0.0126t
40=36.1e^0.0126t
40/36.1 = e^0.0126t
ln(40/36.1) = 0.0126t
ln(40/36.1)/0.0126 = t
8.14 years = t
so,
2005 + 8.14 = 2013
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