The function #f(t)=5(4)^t# represents the number of frogs in a pond after #t# years. What is the yearly percent change? the approximate monthly percent change?

Answer 1

Yearly change: 300%

Approx monthly: 12.2%

For #f(t)=5(4)^t# where #t# is expressed in terms of years, we have the following increase #Delta_Y f# between years #Y+n + 1# and #Y +n#:
#Delta_Y f =5(4)^(Y+n+1) - 5(4)^(Y+n) #
This can be expressed as #Delta P#, a yearly percentage change, such that:
#Delta P =(5(4)^(Y+n+1) - 5(4)^(Y+n))/(5(4)^(Y+n)) = 4 - 1 = 3 equiv 300 \%#
We can then calculate this as an equivalent compounded monthly change, #Delta M#.

Because:

then

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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