The value of a particular item can be modeled by

P(t) = P0(a)t

where P is in dollars and t is the number of years since the item was purchased. Suppose the value of the item increases 5% each year and the item was purchased for $20.

AWrite a formula for P(t) according to the model.

P(t) =

BHow fast is the value of the item increasing when t = 25 years? Round your answer to two decimal places.

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Verified Answer :

FelisFelis FelisFelis · Answer 1 · 2018-10-17T05:33:35-04:00

Answer:

$3.29

Step-by-step explanation:

The value of item increases 5% each year and the item was purchased for $20.00.

A. We have to write a formula for P(t) according to the model:

$P(t)=P_o(1+r)^t$ Where, $P_o$ is the initial price, 'r' is the rate of interest. Here in our case it is compounded annually.

So the formula is:

$P(t)=P_o(1+r)^t$

B. Now we need to find how fast is the value of item increasing when t=25 years.

$P(t)=P_o(1+r)^t$

$P(t)=P_o(1+.05)^t$

$P(t)=P_o(1.05)^t$

Differentiating the function we get the rate of change:

$P'(t)=20 \times (1.05)^t\times ln(1.05)$ (since $P_o=20$)

$P'(t)=20\times 0.0487\times (1.05)^t=0.974(1.05)^t$

Putting t=25, we get:

$P'(25)=0.974(1.05)^{25}=0.974\times3.386=3.29$

So the value of item is increasing by $3.29 each year.

abidemiokin abidemiokin · Answer 2 · 2022-03-01T05:42:40-05:00

The required price after 25 years is $67.73

The required model will be P(t) = 20(1.05)^t

The standard exponential function is expressed as:

P(t) = P0(a)^t

Given the following

Since there is an increment yearly, the required model will be

P(t) = 20(1.05)^t

If t = 25, the required pricee will be calculated as:

P(t) = 20(1.05)^25

P(25) = $67.73

Hence the required price after 25 years is $67.73

Learn more one exponential function here: https://brainly.com/question/12940982