Question

Sort the models based on whether they represent exponential growth or exponential decay.

a) A = A0(0.95)t
b) N = 20,000(1.12)t
c) N = N0ekt, where k 0

Answer 1

A = A0(0.95)^t represents exponential decay, N = 20,000(1.12)^t shows exponential growth, and N = N0e^(kt) with k > 0 also indicates exponential growth.

Step-by-step explanation:

To sort the models based on whether they represent exponential growth or exponential decay, we look at the base of the exponential function. If the base multiplied by the initial amount is greater than 1, it indicates growth; if it's less than 1, it indicates decay.

• The first equation, A = A0(0.95)^t, represents exponential decay because 0.95 is less than 1, meaning with each time period (t), the quantity A gets smaller.
• The second equation, N = 20,000(1.12)^t, shows exponential growth since 1.12 is greater than 1. This causes the quantity N to increase with time.
• The third equation, N = N0e^(kt), where k > 0, suggests exponential growth as well. Since k is positive, the exponent will increase over time, leading to a larger N.

Remembering that an increasing exponent leads to growth, and a decreasing exponent to decay, can help conceptualize these processes.