Answer to Question #112212 in Algebra for Lana

Question

the exponential model describes the population, A, of India, in millions, t years after 1992. A=1072.2e^.012t In which year will India's population be 1653 million?

Answer 1

Given,

A = $1653 \space$millions

We know, one million = $10^6$

A = $1653 \times 10^6$

t = number of years

$A = 1072.2e^{.012t}$

$1653 \times 10^6 = 1072.2 \times e^{0,012\times t}$

$e^{0.012 \times t} = \frac {1653 \times 10^6}{1072.2}$

$e^{0.012 \times t} = 1,541,689.98$

Apply log on both sides

$ln (e^{0.012 \times t}) = ln (1,541,689.98)$

$0.012 \times t = 14.24$

$t = \frac {14.24}{0.012} =1186.66 \approx 1187$

After $1187$ years, the population will becomes $1653$ millions

Hence, year = $1992 + 1187 =3179$