Question

The population of a small town on January 1, 2005, was 7,200. on January 1, 2006, the population was 7,416. On January 1, 2007, the population became 7,639, and on January 1, 2008, the population was 7,867.

Which of the following equations best models the exponential function of this situation?

P(t) =0.3(7,200)(t)

P(t) =7,200(1.03)(t)

P(t) =7,200(t)(1.03)

P(t) =7,200(0.03)(t)

P(t) =7,200(0.97)(t)​

Answer 1

(b) P(t) =7,200(1.03)^(t)

Explanation:

The multiplier each year for the population is about ...

7416/7200 = 1.03

The initial value is 7200, so the exponential function can be written as ...

P(t) = 7200×1.03^t

_____

Additional comment

In plain text, the exponent is signified by a caret (^). Without it, the expression becomes a linear function. In typeset text, the exponent should be in a superscript font. (We notice that curriculum materials do not always properly represent exponential functions.)