Compound Interest Equation help?

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dancer12

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The population of a city 10 years ago was 150,000. Since then, the population has increased at a steady rate each year. The population is currently 185,000.

a) Write an exponential function that could be used to model the population after x years if the population changes at the same rate.
b) What will the population be in 25 years?

The equation that needs to be used is: A= P(1+ (r/n))^nt
 
Are you sure? That is not a compound interest problem.

It's just P = 150000 a^t, and you already know
185,000 = 150,000 • a^10 so solve for a
185/150 = a^10
(185/150) ^ (1/10) = a = (37/30)^(1/10)

so P = 150,000 (37/30) ^ (t/10)

and in 25 years, P = 150,000 (37/30) ^ (25/10) or about 253,392
 
A is the final value (185,000)
P is the original value (150,000)
R is the rate
N is the number of periods (1 year per year, so 1 (when using months, use 12 here))
T is the time (25)

Plug in the numbers, and solve for R. Then convert from a number to a percentage.
 
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