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.

AP = 145e10k

BP = 145e20k

CP = 190e10k

DP = 190e20k

Verified Answer :

Answer: Option B is correct

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

\(P=145e^{20k}\\\)

Step-by-step 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

\(P=145e^{20k}\\\)

\(2^{nd}\) Option

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