The population of Leavetown is 123,000 and is decreasing at a rate of 2.375% each year. • When will the population of Leavetown drop below 50,000 (to the nearest year)? • What will the population of Leavetown be 100 years from now?

123,000 x 2.375% = 2,921.25. This gives you the rate that the population is decreasing. How long will it take to get to 50,000. Do reverse operations to find this answer: 123,000 - 50,000 = 73,000, the population need to decrease by 73,000 to get to 50,000. So let's multiply our rate of 2,921.25 x 25 = 73,031 and our final step.. 123,000 - 73,031 = 49,969 below 50,000

raphealnwobi raphealnwobi · Answer 2 · 2021-12-16T11:33:49+01:00

The population of Leavetown 100 years from now is 11118

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

Let y represent the population of leave town after x years.

The population of Leavetown is 123,000 and is decreasing at a rate of 2.375%. Hence:

a = 123000, b = 100% - 2.375% = 0.97625

The exponential function becomes:

y = 123000(0.97625)ˣ

For a population of 50000:

50000 = 123000(0.97625)ˣ

0.4065 = (0.97625)ˣ

ln(0.4065) = xln(0.97625)

x = 37 years

It takes 37 years to reach a population of 50000

For 100 years:

y = 123000(0.97625)¹⁰⁰ = 11118

The population of Leavetown 100 years from now is 11118

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