Need algebra help with a function, p(t) that is measured in $ and where t is the number of years from today

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Dec 17th, 2015

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We are given a function of t as:

p(t) = 800(1.019)^t

First Part:

 To find the initial price of the item, put t=0

So we get P(0) = 800(1.019)^0

P(0) = 800*1

P(0) = 800

Hence initial price is $800.

Second Part:

Since it is a positive exponential function, so function represents growth only.

Third Part:

At t years price: p(t) = 800(1.019)^t

At t+1 years price: p(t+1) = 800(1.019)^(t+1)

So % change = [{p(t+1) - p(t)}/p(t)]*100

% change = [{800(1.019)^(t+1) - 800(1.019)^t}/800(1.019)^t] * 100

Taking 800(1.019)^t as common, we get

% change = [{800(1.019)^t *(1.019-1)}/800(1.019)^t]*100

Cancelling out the common factor, we get

% change = (1.019-1)*100

So % change = 1.9%

Therefore % change in price each year is 1.9%

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 17th, 2015

Dec 17th, 2015
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