Answer:
3840 pairs of shoes
Explanation:
To write an exponential model that relates the number of shoes sold to the week number, we can use the general form of an exponential function:
y = a * b^x
where:
y is the number of shoes sold,
x is the week number, and
a and b are constants to be determined.
Given the information:
In week 0, 30 pairs of shoes were sold.
In week 3, 240 pairs of shoes were sold.
We can use these two data points to determine the values of a and b.
Using the data point for week 0:
30 = a * b^0
30 = a
Using the data point for week 3:
240 = 30 * b^3
8 = b^3
b = 2 (taking the cube root of both sides)
Therefore, the exponential model that relates the number of shoes sold to the week number is:
y = 30 * 2^x
To predict the number of shoes sold during week 7, we substitute x = 7 into the model:
y = 30 * 2^7
y = 30 * 128
y = 3840
Therefore, the model predicts that 3840 pairs of shoes will be sold during week 7.