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 = $1992 + 1187 =3179$