Question

Which country has a decreasing population? By what percentage us the population of that country decreasing each year?

India: `A = 1049.7e^0.015t`
Iraq: `A = 24.7e^0.028t`
Japan: `A = 127.2e^0.001t`
Russia: `A= 144.5e^-0.004t`

Answer 1

Russia is the only one with a decreasing population curve. It is decreasing at a rate of `0.40%`

Explanation:

Russia is the only expression with a negative in the exponential term, indicating a decrease. To find the percentage decrease you can calculate the value for two different years.

`A=144.5e^(−0.004t)`

`A_1=144.5e^(−0.004) = 143.92`

`A_2=144.5e^(−0.008) = 143.35`

The percent change is thus:
`(143.92 - 143.35)/143.92 = 0.00397`
`100 xx 0.00397 = 0.40%`