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?

Answer 1

`f(a_n) = 0.7f(a_(n-1)) + 25`

Explanation:

The number of t-shirts a in month n is 70% of the number of t-shirts in month n-1 plus 25 because they always sell 30% of the t-shirts and get 25 t-shirts in shipments.
`f(0)=100` can be included as an after-thought.

Answer 2

Answer: The recursive formula is given by

`f(a_n)=0.70f(a_(n-1))+25`

Explanation:

Since we have given that

Number of t-shirts = 100

f(0) = 100

Each time there is 30% of the t-shirt were sold and 25 new t-shirts arrived in shipments.

So, it becomes,

`f(a_n)=(1-0.30)f(a_(n-1))+25\\\\f(a_n)=0.70f(a_(n-1))+25`

Hence, the recursive formula is given by

`f(a_n)=0.70f(a_(n-1))+25`