Question

For the following, state which situation models an exponential function and which does not. Explain your

reasoning in a few sentences.
Situation 1- Every day the number of bacteria on a washcloth increases by 0.5% from the previous day.
Situation 2- Every week a store gives out 2 coupons to its customers.

Answer 1

situation 1

Explanation:

it starts with a number b of bacteria.

to grow by 0.5% means to multiply b by 1.005 (= 1 + 0.005) :

day1 = b

day2 = day1 × 1.005

the next day we multiply that by 1.005

day3 = day2 × 1.005 = day1 × 1.005²

so, we get

dayn = dayn-1 × 1.005 = day1 × 1.005^(n-1)

so, the function to calculate the number of bacteria after n days is

f(n) = b × 1.005^(n-1)

the variable of the function is in the exponent, which makes it an exponential function.

in situation 2 we simply have the function f to calculate the number of coupons issued

f(n) = 2n