SOLUTION: 5. Modeling Population: The population of the world has grown rapidly during the past century. As a result, heavy demands have been made on the world's resources. Exponential funct

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Question 826467: 5. Modeling Population: The population of the world has grown rapidly during the past century. As a result, heavy demands have been made on the world's resources. Exponential functions and equations are often used to model this rapid growth, and logarithms are used to model slower growth. The formula models the population of a US state, A, in millions, t years after 2000.
a. What was the population in 2000?
b. When will the population of the state reach 23.3 million?
The population in the year 2000 of state "A," according to the equation, was:
16.6e^0.547(0), or 16.6e^0, or 16.6 million.
Answer Part a:
16.6 million
could you please help solve for part b please
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
A=16.6%2Ae%5E%280.547%2At%29, for t years after year 2000, A in millions is the population at time t, 16.6 is population in millions at time t=0.

Part b: When will A=23.3 ?
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Solve the equation for t, and then just substitute A=23.3.
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Take natural logarithm of both sides;
ln%28A%29=ln%2816.6e%5E%280.547t%29%29
ln%28A%29=ln%2816.6%29%2Bln%28e%5E%280.547t%29%29
ln%28A%29=ln%2816.6%29%2B0.547t%2Aln%28e%29
DO you know what to do from here?