a math problem i don't understand

Question

Which of the contexts below could not be modeled by an exponential function?

a An coin collection appreciates at a rate of 17.2% per year.

b A music service has a fixed monthly cost and charges $0.20 for each downloaded song.

c A car depreciates at a rate of 2.7% per year.

d Money invested in a savings account grows at an annual rate of 3.4%.

Answer 1

answer they're looking for is b)

all except b) can be modeled with an exponential function

a) A(t) = Pe^.172t = coin collection value in year t

general formula is

A(t) = Pe^rt where r = annual interest or growth rate, t = number of years

it's a fomula for continous compounding.

c) A(t = Pe^-.027t = car value in year t.

the negative sign in the exponent indicates decay or negative growth

i

d) A(t) = Pe^.034t for continuously compounded interest or

A(t) = P(1.034)^t for annually compounded interest. both are exponential functions. The exponent is a variable, t = number of years

b) A(m) = m + .2s is a linear equation, not exponential.

If you wanted to be very petty, ridiculous and trivial,

you could write it in degenerate "exponential"

form with an e^(0)t factor, but that just =1 and is redundant surplusage.

when annual rate of change =0%, there is no growth or decay

A(m) = me^(0)t + .2s = m(1) +.2s = m+.2s

A = ending Amount, P = starting value