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If the population of a small city is45,000.If the population grows continuously by5%per​ year, in how many years will the population reach75,000​?

Question

If the population of a small city is

45,000.

If the population grows continuously by

5%

per​ year, in how many years will the population reach

75,000​?
check_circleAnswer
Step 1

Here we use compound interest based formula. If p is present population, r is rate of growth of population  and P is the population after n years.

r
P p1+
100
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r P p1+ 100

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Step 2

We substitute p=45000, P=75...

P p1
100
5
75000 45000 1+
100
750001.05)
45000
1.6667 (1.05
In (1.6667) nln1.05
In(1.6667) 0.51084 10.5
In (1.05)
0.04879
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P p1 100 5 75000 45000 1+ 100 750001.05) 45000 1.6667 (1.05 In (1.6667) nln1.05 In(1.6667) 0.51084 10.5 In (1.05) 0.04879

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Math

Calculus

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