<PRE><B>Question 1146528</B>
the exponential growth formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is he interest rate per time period
n is the number of time periods.


in your problem, the formula becomes 25000 = 2100 * (1 + r) ^ 18
divide both sides of this equation by 2100 to get:
25000/2100 = (1 + r) ^ 18
take the 18th root of both sides of the equation to get:
(25000/2100) ^ (1/18) = 1 + r
subtract 1 from both sides of the equation to get:
(25000/2100) ^ (1/18) - 1 = r
solve for r to get:
r = .1475252801
multiply by 100 to get 14.75252801%.


that is the annual rate of growth.
replace r in the original equation to get:
25000 = 2100 * (1+.1475252801)^18
evaluate to get:
25000 = 25000
this confirms the annual rate of growth is correct.


the annual rate of growth is 14.75252801%


the common ratio sounds like it would be 1.1475252801.


each year, the population of pavement ants grows by that factor.
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