Question

1. which of the three situations given below is best modeled by an exponential function?

i. a bacteria culture doubles in size every day.
ii. a plant grows by 1 inch every 4 days.
iii. the population of a town declines by 5% every 3 years.
(1) i, only
(2) ii, only
(3) i and ii
(4) i and iii

Explanation:

Step1: Identify exponential growth/decay

Exponential models describe percent change per period (not constant additive change).

Step2: Analyze Situation I

Bacteria doubles (100% growth) daily: exponential.
Model: $P(t) = P_0 \times 2^t$

Step3: Analyze Situation II

Plant grows 1 inch (constant additive change) every 4 days: linear, not exponential.
Model: $h(t) = h_0 + \frac{1}{4}t$

Step4: Analyze Situation III

Town population declines 5% (percent change) every 3 years: exponential decay.
Model: $P(t) = P_0 \times (0.95)^{\frac{t}{3}}$

Step5: Select valid situations

Situations I and III are exponential.

Answer:

(4) I and III