A town has a population of 20000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 42800?

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Mathematics

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25 December, 13:56

A town has a population of 20000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 42800?

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Answers (1)

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Arthur Murphy · Answer 1

Answer:17.3 years

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

A = P (1 + r) ^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

A = 42800

P = 20000

r = 4.5% = 4.5/100 = 0.045

Therefore

42800 = 20000 (1 + 0.045) ^t

42800/20000 = (1.045) ^t

2.14 = (1.045) ^t

Taking log of both sides to base 10

Log 2.14 = log1.045^t = tlog1.045

0.3304 = t * 0.0191

0.3304 = 0.0191t

t = 0.3304/0.0191

t = 17.3 years