Question

Supposed that the future price p(t) of a certain item is given by the following exponential function.inthis function, p(t) is measured in dollars and t is the number of year's from today. p(t)= 2500 (1.026)t

Answer 1

Initial price of the item = 2500

The function represents growth

The percent by which the price changes each year is 2.6%

Step-by-step explanation:

The given function is expressed as

P(t) = 2500(1.026)^t

Recall, the exponential growth function is expressed as

P(t) = Po(1 + r)^t

where

Po is the initial value

P(t) is the future value

r is the growth rate

By comparing both functions,

Po = 2500. Thus,

Initial price of the item = 2500

Also,

1 + r = 1.026

Since 1.026 is greater than 1,

The function represents growth

r = 1.026 - 1

r = 0.026

This means that the growth rate is 0.026. We would convert it to percentage by multiplying by 100. It becomes

0.026 x 100 = 2.6%

The percent by which the price changes each year is 2.6%