)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.

The value of 'k' will be 0.031

Explanation

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

, where 'a' is the population in years after 1984.

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

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

(Rounded up to three decimal places)

So, the value of 'k' is 0.031

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).