Digital SAT® Practice Test 1: Math Module 1: Question 5 Explanation

Digital SAT Math Test 2 Question 5

A wildfire can spread triple the area every hour. The size of the wildfire was 10 acres when it was first detected. Which represents the size of the fire,

A

, in acres

t

hours after the first detection?

$A = 10 (\frac{1}{3})^{t}$
$A = \frac{1}{3} (10)^{t}$
$A = 3 (10)^{t}$
$A = 10 (3)^{t}$

Answer:

Explanation

The correct answer is Choice D.

Use the given information to construct an equation for the size of the wildfire, $A$ , $t$ hours after it was first detected.

Choice A is incorrect because the factor of growth is less than $1$ which means that the size of the fire will decrease each hour.

Choices B and C are incorrect because $10$ is the initial size of the wildfire and not the factor of growth.

✨ Expert's Tip ✨

In an exponential equation $y = A_{0} (B)^{\frac{t}{c}}$ , $A$ is the initial value, $B$ is the growth factor, and $C$ is the period.