Question

Can someone check this for me?

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * at where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you prefer that the value of be between 0 and 1 or larger than 1? Explain your reasoning.

C = p *a^t

C = ?

P = 10 cars

T = 10 months

A = 0

C = 15(0)^10
C = 15(0)
C = 0

Answer 1

If a is greater than one, the number of cars on the road every day will get bigger and bigger, say a = 1.5
day 1 p*1.5
day 2 p*2.25

If a is smaller than one, c will get smaller every day after start, say a = .5
day 1 .p*.5
day 2 P*.25
day 3 p*.125