Question

A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100? A. f(n) = f(n - 1) • 0.3 + 25, n > 0 B. f(n) = 100 - f(n - 1) • 0.3 + 25, n > 0 C. f(n) = f(n - 1) • 0.7 + 25, n > 0 D. f(n) = 100 - f(n - 1) • 0.7 + 25, n > 0

Answer 1

If 30% of the t-shirts are sold, then f(n) includes f(n-1)*0.7.  If we add 25 new t-shirts, the total value of f(n) is f(n-1)*0.7+25.  C is the correct answer.

Answer 2

recursive function best represents the number of t-shirts in the store, given that f(0) = 100 is:

f(n) = f(n - 1)×0.7 + 25,n > 0.

Explanation:

A store had 100 t-shirts i.e. f(0) = 100.

Each month, 30% of the t-shirts were sold this means that each month the t-shirts left are 70% i.e. 0.7 of the total shirts in that month.

Also 25 new t-shirts arrived in shipments.

This means that at the end of month the t-shirts in the store will be 0.7 times the t-shirts in start of that month plus 25.

Hence, the expression that best represents this problem is given by:

f(n) = f(n - 1)×0.7 + 25,n > 0.

Where n represents the month.