Question

The population of a town is increasing at an annual rate

of 6.2%. the city council believes they will have to add
another elementary school when the population reaches
110,000. if there are currently 56,000 people living in
the town, how long do they have before the new school
will be needed to the nearest tenth of a year?
[ use a = p(1 + r)']
(1) 11.2
(2) 1.8
(3) 109.2
(4) 3.2

Answer 1

Okay, let's solve this step-by-step:

* The population is increasing at an annual rate of 6.2%, which means the growth rate (r) is 0.062.

* The initial population (p) is 56,000

* They need to build a new school when the population reaches 110,000

* Using the formula a = p(1 + r)^t where:

- a is the future population (110,000)

- p is the initial population (56,000)

- r is the growth rate (0.062)

- t is the number of years

Plugging in the values:

110,000 = 56,000(1 + 0.062)^t

Solving for t:

t = ln(110,000/56,000)/ln(1 + 0.062)

t = ln(1.964)/ln(1.062)

t = 10.9 years → to the nearest tenth, that is 11.0 years

So the answer is (1) 11.2