Question

Maria needs to write thank-you cards for the gifts she received at her quinceañera. She has a total of 50 cards to write and estimates that she can write 2 cards in 5 minutes. You can use a function to approximate the number of thank-you cards Maria will still need to write after x minutes.
Write an equation for the function. If it is linear, write it in the form g(x)=mx+b. If it is exponential, write it in the form g(x)=a(b)x.

Answer 1

She writes 2 cards every 5 minutes, i.e. 2/5 = 0.4 cards per minute. After x minutes she has written 0.4x cards, so the number remaining is

g(x) = 50 − 0.4x.

This is linear, in the form g(x) = mx + b with m = −0.4 and b = 50. (Valid for 0 ≤ x ≤ 125, when g(x) ≥ 0.)