High School

A store had 150 laptops in the month of January. Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store.

Which recursive function best represents the number of laptops in the store \( f(n) \) after \( n \) months?

A. \( f(n) = 150 - 0.8 \times f(n - 1) + 10, \, f(0) = 150, \, n > 0 \)

B. \( f(n) = 0.2 \times f(n - 1) + 10, \, f(0) = 150, \, n > 0 \)

C. \( f(n) = 0.8 \times f(n - 1) + 10, \, f(0) = 150, \, n > 0 \)

D. \( f(n) = 150 + 0.8 \times f(n - 1) + 10, \, f(0) = 150, \, n > 0 \)

Answer :

Answer:

Option C is the correct answer.

Step-by-step explanation:

Let us find the amount of laptops available.

n = 0, Laptops = 150

n = 1 , Laptops = 150 - 0.2 x 150 + 10 = 0.8 x 150 + 10 = 130

n = 2, Laptops = 130 - 0.2 x 130 + 10 = 0.8 x 130 + 10 = 114

So we have f(0) = 150.

f(1) = 0.8f(0)+10

f(2) = 0.8f(1)+10

Similarly f(n) = 0.8f(n-1)+10

Option C is the correct answer.
N. f(n)
0 150
1 .8 (150)+10
2. ......

The answer is c

hoping this helps

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