Question

Suppose the population of a country in 1985 was 145 million. In 1995 it was 190 million. Use the formula P = Ae kt to setup an expression to estimate the population of the country in 2005.

A. P = 145e10k

B. P = 145e20k

C. P = 190e10k

D. P = 190e20k

Answer 1

`2^(nd)` Option

`\left[\begin{array}{ccc}P=145e^((0.027)(10))\\P=145e^{(0.027)(20)\\P=190e^((0.027)(10))}\\P=190e^{(0.027)(20)\end{array}\right]`

Answer 2

Answer: Option B is correct

The expression to estimate the population of the country in 2005 is given by

`P=145e^(20k)\\`

Explanation:

Since we have given that

In 1985, there was population of 145 millions.

Similarly,

In 1995, there was a population of 190 million .

Use the formula,

`P=Ae^(kt)\\`

where A denotes the initial population and t denotes the number of years.

So, the expression becomes

`P=145e^(20k)\\`

∵ time period between 1985 to 2005 is 20 years.

So we take t=20 years.

So, the expression to estimate the population of the country in 2005 is given by

`P=145e^(20k)\\`