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Answer:
It will take 9 years for the population to double
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.
Substituting in the equation:
[tex]2P_o=P_o(1+0.08)^t[/tex]
Simplifying:
[tex]2=(1.08)^t[/tex]
Taking logarithms:
[tex]\log 2=\log (1.08)^t[/tex]
Applying the exponent property of logs:
[tex]\log 2=t\log (1.08)[/tex]
Solving for t:
[tex]\displaystyle t=\frac{\log 2}{\log (1.08)}[/tex]
Calculating:
[tex]t\approx 9[/tex]
It will take 9 years for the population to double