Problema Solution
The word problem A=15.7e^0.0407t models the population of a U.S. state, A, in millions, t years after 2000.
A. In 2000, the population of the state was ___ Million
B. The population of the state will reach 18.7 million in the year ____
Answer provided by our tutors
A=15.7*e^(0.0407t)
A. In 2000 we have t=0
A=15.7*e^(0.0407*0)
A = 15.7 million
In 2000, the population of the state was 15.7 Million
B. we have A = 18.7 million we need to find t
18.7=15.7*e^(0.0407t)
e^(0.0407t) = 18.7/15.7
0.0407t = ln (18.7/15.7) divide both sides be 0.0407
t = (1/0.0407)*ln (18.7/15.7)
t = 4.296 years
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The population of the state will reach 18.7 million in the year 2004.