Question

) the population of a particular country was 25 million in 1984; in 1992, it was 32 million. The exponential growth function a = 25ekt describes the population of this country t years after 1984 . Use the fact that 8 years after 1984 the population increased by 7 million to find k to three decimal places.

Answer 1

The value of 'k' will be 0.031

Step-by-step explanation

The population of a particular country was 25 million in 1984. The exponential growth function is .....

`a= 25e^k^t` , where 'a' is the population in
`t` years after 1984.

In 1992, the population was 32 million. That means,
`a= 32 million` for
`t=8` years. So, plugging those values of 'a' and 't' into the above equation, we will get......

`32=25e^8^k\\ \\ e^8^k= (32)/(25)`

By taking natural logarithm on both sides, we will get...

`ln(e^8^k)= ln((32)/(25))\\ \\ 8k*ln(e)=ln((32)/(25))\\ \\ 8k= ln((32)/(25))\\ \\ k= (ln((32)/(25)))/(8)=0.03085....\\ \\ k= 0.031`

(Rounded up to three decimal places)

So, the value of 'k' is 0.031