the value of a textbook is 79$ and decreases at a rate of 15% per year

Question

the value of a textbook is 79$ and decreases at a rate of 15% per year

Answer 1

These type of problems would as us to find the value of the textbook after a certain number of years. So for this problem, we will find the value of the textbook in 5 years.

The formula used for rates of decay (decreasing value) and rates of growth (increasing value) is:

y = ab^x where

y = new value

a = original value

b = rate of change = 1 + r

x = time

From the problem, we are looking for the value of y, it is given that a = 79, and x = 5

To find b, we need to find r by converting the percentage value to a decimal value. 15% = 0.15. Since this a decreasing rate, r = -0.15 Note: if the textbook value was increasing, the value of r would be 0.15

So b = 1 - 0.15 = 0.85

Plug all our known values into the equation and we get:

y = 79(0.85)⁵ Be careful to follow the rules of operation.

y = 79(0.4437) On paper, round to 4 decimal places, but don't round on the calculator)

y = 35.05 Since we are dealing with money, round to nearest penny.

The value of the textbook after 5 years will be $35.05.

Side note: You might see a similar problem to this one using actual year number like 2019 instead of time frames like the 5 years in this problem. If this problem asked you what the value of the textbook would be in 2024 instead of 5 years from now, you will need to make a small calculation to find t. DO NOT USE 2024 for t. That would represent the value of the textbook 2,024 years from now, not the year 2024. To find t, simply determine how many years the target year is from the present. t = 2024 - 2019 = 5