Question 1202338: At first there were 17 boring beetles. The number of boring beetles doubled every day.
(a) Write an equation that describes the number of beetles there would be after n days.
(b) Using the equation in (a), determine the number of beetles there would be after 30 days.
Answer by math_tutor2020(3817)   (Show Source):
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Answers:
(a) P = 17*2^n
(b) 18,253,611,008 (roughly 18.25 billion)
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Explanation for Part (a)
One possible exponential equation template is P = a*b^n
where,
n = number of days
P = number of beetles
a = starting amount
b = growth rate when b > 1
In this case,
a = 17
b = 2, meaning the population doubles each time n goes up by 1.
We go from P = a*b^n to P = 17*2^n
If n = 0, then P = 17
If n = 1, then P = 34
If n = 2, then P = 68
and so on.
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Explanation for Part (b)
Plug n = 30 into the equation we just found.
P = 17*2^n
P = 17*2^30
P = 18,253,611,008
This population count is roughly 18.25 billion.
I don't know much about beetles, or insects, to know if this population count is realistic or not.
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