Question

The value of a rare coin y (in dollars) can be approximated by the model y= 0. 25 (1. 06)^t, where t is the number of years since the coin was minted.

a. Tell whether the model represents exponential growth or exponential decay.

b. Identify the annual percent increase or decrease in the value of the coin.

c. What was the original value of the coin?

d. Estimate when the value of the coin will be $0. 60

Answer 1

a) The model represents the exponential growth.

b) The annual percentage increase in the value of the coin is 106%.

c) The original value of the coin is; 0.25.

d) The value of the coin would be $0.60 when the time, t is; 15 years.

Exponential growth functions

It follows from the equation given in the task content that;

• The model represents the exponential growth as indicated by the increase in the value of the coin with time.
• The annual percentage increase is therefore 106 percent, as the value of the coin increases by a factor of 1.06 each year.
• The original value of the coin would be $0.25 as this indicates the value of the coin at time t= 0.
• When the value of the coin is $0.60, then;

0.60 = 0.25(1.06)^t

• (1.06)^t = 2.4

• t = 0.3802/0.0253

• t = 15.03years

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