Answer:
a) 23.1 million
b) year 2013
Explanation:
Given a population in millions is modeled by A = 23.1e^(0.0152t) for t years after 2000, you want to know the population in year 2000, and the year in which the population is 28.3 million.
a) Initial population
When t=0, the exponential factor is 1. The population is given by the coefficient of that factor: 23.1
The population in 2000 was 23.1 millions.
b) Year of 28.3M
We can solve for t to find the year the population is 28.3 million:
28.3 = 23.1e^(0.0152t)
28.3/23.1 = e^(0.0152t) . . . . .divide by 23.1
ln(28.3/23.1) = 0.0152t . . . . . take natural logs
t ≈ 13.36
The population will reach 28.3 million in the year 2013.
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