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

Respuesta :

Answer: Option B is correct

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

[tex]P=145e^{20k}\\[/tex]

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,

[tex]P=Ae^{kt}\\[/tex]

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

So, the expression becomes

[tex]P=145e^{20k}\\[/tex]

∵ 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

[tex]P=145e^{20k}\\[/tex]

[tex]2^{nd}[/tex] Option

[tex]\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][/tex]