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
Algebra ->
Testmodule
-> 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
Log On
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?
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.
