Question

1. shayla invests $500 at her local bank. the amount of money in her account every year is shown in the table below. which exponential equation represents this scenario?

time in years | 1 | 2 | 3
amount of money in the account | $525 | $551.25 | $578.81
options:
$y = 1.050(500)^n$
$y = 500(0.95)^n$
$y = 500(1.05)^n$
$y = 500(0.05)^n$

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth equation is \( y = a(1 + r)^n \), where \( a \) is the initial amount, \( r \) is the growth rate, and \( n \) is the time. Here, the initial investment \( a = 500 \).

Step2: Calculate the growth factor

To find the growth factor, divide the amount in year 2 by year 1: \( \frac{551.25}{525}= 1.05 \). Or divide year 3 by year 2: \( \frac{578.81}{551.25}\approx1.05 \). So the growth factor \( (1 + r)=1.05 \).

Step3: Identify the correct equation

Using the exponential growth formula with \( a = 500 \) and growth factor \( 1.05 \), the equation is \( y = 500(1.05)^n \).

Answer:

\( y = 500(1.05)^n \) (the third option)