a The product of the original value and the multiplier multiplied three times should equal the final value.
B
b An exponential function is always of the form y=ab^x, where a is the initial value and b is the multiplier.
A
a 73 %
B
bFunction: y=500(0.27)^x
Explanation: See solution.
Practice makes perfect
a If we call the annual multiplier m, the original value of 500 multiplied by m three times should equal the poster's value after three years. With this information, we can write the following equation.
500(m)(m)(m)=10If we solve for m, we can find the annual multiplier.
The multiplier is 0.27. If we subtract this from 1, we can determine the annual rate of depreciation.
1-0.27=0.73
The annual rate of depreciation is 73 %.
b We want to write a function which allows us to calculate the value of the poster after x years. Since we know that to find the value of the poster one year from today, we should multiply today's value by the annual multiplier. Our function will be an exponential one.
y = ab^x
In the equation above, a is the initial value and b is the multiplier. We know that at the band's peak of popularity the poster cost $500. Also, we know from Part that 0.27 is the multiplier. Assuming that $500 is the initial value, we can write the following formula.
y = 500( 0.27)^x
Here x represents the number of years that passed since the band's peak of popularity.
