As a promotion, a store draws the name of a customers each week. The prize is a coupon for the store. If winner is not present at drawing, he cannnot claim the prize and the amount of the coupon increases for the next weeks drawing. the function f(x)= 20(1.2)to the x power, gives the amt of the coupon in dollars after x weeks of the prize going unclaimed.
a. what is the amt of the coupon after 2 wks of prize not claimed?
b.after how many weeks of the prize going unclaimed will the amt of the coupon be greater than $100?
c. What is the original amt of the coupon?
d. Find the percent increase each week?
I am having trouble solving d. Please help
A. Since f(x)=20(1.2)^x, substitute x for 2 as for 2 weeks. f(2) = 20(1.2)^2 = 20(1.44) = $28.80.
B. Using the guess and check method on a table, f(x)=20(1.2)^x, f(0)=20, f(1)=24, f(2)=28.8, f(3)=34.56, f(4)=41.472, f(5)=49.7664, f(6)=59.71968, f(7)=71.663616, f(8)=85.9963392, f(9)=103.195607, and 103.195607>100. So, it will take 9 weeks for the prize to be greater than $100 going unclaimed.
C. From f(x)=a(1+r)^x, where a is the initial value and r is the rate of change, and f(x)=20(1.2)^x, $20 would be the original amount of the coupon.
D. From f(x)=a(1+r)^x, where a is the initial value and r is the rate of change, and f(x)=20(1.2)^x, 20% would be the percent increase each week.
To find the percent increase each week, we need to compare the amount of the coupon for each week to the previous week. We'll use the formula:
Percent Increase = (New Value - Old Value) / Old Value * 100
In this case, the amount of the coupon after x weeks is given by the function f(x) = 20 * 1.2^x.
Let's calculate the percent increase for each week:
Week 1: The original amount of the coupon is f(0) = 20 * 1.2^0 = 20 dollars.
There is no previous week, so the percent increase for the first week is 0%.
Week 2: The amount of the coupon after 2 weeks is f(2) = 20 * 1.2^2 = 28.8 dollars.
The previous week's amount was 20 dollars.
Percent Increase = (New Value - Old Value) / Old Value * 100 = (28.8 - 20) / 20 * 100 = 44%.
Therefore, the percent increase each week is 44%.