SOLUTION: MAT 145: Topics In Contemporary Math 19: Solving Exponential Growth 1) The population of fuzzy quadrupeds doubles every month after they are introduced to a

Question 1193275: MAT 145: Topics In Contemporary Math
19: Solving Exponential Growth

1) The population of fuzzy quadrupeds doubles every month after they are introduced to a
new region. Suppose 5 fuzzy quadrupeds are accidentally introduced to Springfield when
a family visited the region to which fuzzy quadrupeds are native. How many months
would it take for there to be 325 fuzzy quadrupeds in Springfield?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
growth factor = 2 per month
formula is f = p * g ^ n
f is the future value
p is the presen value
g is the growth factor per time period
n is the number of time periods
in t his problem:
f = 325
p = 5
n = number of months.
g = growth factor = 2 per month.
formula becomes 325 = 5 * 2 ^ n
divide both sides of this equation by 5 to get:
325 / 5 = 2 ^ n
take the log of both sides of the equation to get:
log(325/5) = log(2^n)
by log rules, this becomes:
log(325/5) = n * log(2)
divide both sides of the equation by log(2) and solve for n to get:
n = log(325/5) / log(2) = 6.022367813.
confirm by replacing n in the original equation by that to get:
f = 5 * 2 ^ 6.022367813 = 325, confirming the value of n is good.
your solution is that it would take 6.022367813 months for the 5 fuzzy quadrupeds to grow to 325.
that would be in the 7th month.
here's what it looks like on a graph.

the unshaded area of the graph is between the end of month 6 and the end of month 7.
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