Question

question #4
which situation could be modeled by a linear function?
(1) the value of a car depreciates by 7% annually.
(2) a gym charges a $50 initial fee and then $30 monthly.
(3) the number of bacteria in a lab doubles weekly.
(4) the amount of money in a bank account increases by 0.1% monthly.

Explanation:

A linear function has a constant rate of change (no exponential growth/decay).

1. Car depreciation by 7% annually is exponential decay: $V(t)=V_0(0.93)^t$.
2. Gym fees have a fixed initial cost plus a constant monthly rate: $C(m)=50+30m$, which is linear.
3. Bacteria doubling weekly is exponential growth: $N(t)=N_0(2)^t$.
4. Bank account growth by 0.1% monthly is exponential growth: $A(t)=A_0(1.001)^t$.

Answer:

(2) A gym charges a $50 initial fee and then $30 monthly.