Question

A town has a population of 19000 and grows at 4.5% every year. To the nearest tenth

of a year, how long will it be until the population will reach 49000?

Answer 1

Answer: 21.5 cause i got the answer wrong and they gave me the correct answer

Answer 2

33.1 years

Explanation:

Let x be the number of years it takes for the population to reach 49000.

Starting with a population of 19000 and growing at 4.5% per year, the population after t years can be represented by the exponential function:

P(x) = 19000(1 + 0.045)^x

We want to find the value of x that makes P(x) = 49000.

=> 49000 = 19000(1 + 0.045)^x

Dividing both sides by 19000, we get:

=> 2.57895 = 1.045^x

Taking the logarithm of both sides with base 10, we get:

=> log(2.57895) = x log(1.045)

=> x = log(2.57895) / log(1.045)

=> x ≈ 33.1

Therefore, it will take approximately 33.1 years for the population to reach 49000.