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The population of a city is 430​,000 and is increasing at a rate of 4.25​% each year. Approximately when will the population reach 860​,000? ​ (Use a compound growth​ model.)

User Nahab
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1 Answer

4 votes

Answer:

The population will reach 860,000 in 16.67 years from now.

Explanation:

The compound growth model is given by the following equation:


P(t) = P(0)(1+r)^(t)

In which
P(0) is the initial population and r is the growth rate(decimal).

In this problem, we have that:


P(0) = 430000, r = 0.0425

Approximately when will the population reach 860​,000?

This is t when
P(t) = 860000. So


P(t) = P(0)(1+r)^(t)


860000 = 430000(1+0.0425)^(t)


(1.0425)^(t) = (860000)/(430000)


(1.0425)^(t) = 2

We have the following logarithm rule


\log{a^(t)} = t\log{a}

Applying log to both sides


\log{(1.0425)^(t)} = \log{2}


t\log(1.0425) = 0.3


0.018t = 0.3


t = (0.3)/(0.018)


t = 16.67

The population will reach 860,000 in 16.67 years from now.

User Ckhan
by
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