Question

A group of students is discussing situations that can be modeled by exponential decay. Which of the following students are correct? Select ALL that apply.

a- The final value is larger than the initial value.
b- The final value is smaller than the initial value.
c- The base is less than 1 but greater than 0
d- The base is greater than 1.

Answer 1

Exponential decay is correctly represented by situations where the final value is smaller than the initial value, and the base of the exponential function is between 0 and 1. Carbon-14 decay is an example of exponential decay, with a graph that would show the amount of Carbon-14 decreasing over time at a specified decay rate.

Step-by-step explanation:

In situations modeled by exponential decay, the following are correct:

• The final value is smaller than the initial value.
• The base is less than 1 but greater than 0.

Additionally, when discussing exponential growth or decay, remember that

• As the number N decreases in magnitude, the exponent increases, and vice versa.

For example, with Carbon-14 decay, which has a half-life of about 5,730 years and a decay rate of 0.000121, one can model its exponential decay over time. The value of Carbon-14 over time would be represented on the y-axis, and time in years on the x-axis, with the decay rate indicating the rate of decrease.