The formula for the exponential function is y = a * b^x, where a is the initial value and b is the multiplier. To find the annual percent of decrease, subtract b from 1 and multiply the result by 100 %.
15 %
Practice makes perfect
We want to find the annual percent of decrease in the following situation.
Principal's New Car:& $35 000
Value After3 Years:& $21 494
Let's start by recalling the formula for the exponential function.
y = a * b^x
In this formula, a represents the initial price and b is the multiplier. In order to find the percent of decrease, we will first find the value of b. From the exercise we know that the initial price of the car, the value at b^0, is $35 000 and after 3 years its value drops to $21 494. This allows us to write the following system of equations.
35 000 = a * b^0 & (I) 21 494 = a * b^3 & (II)
Let's find the value of b in this system. Notice that if we were to divide Equation (II) by Equation (I) and simplify, we will have an equation only with b as a variable.
21 494/35 000=a* b^3/a* b^0 ⇔ 21 494/35 000=b^3/b^0
Let's solve for b!
