Question

the number of students enrolled at a college is 15,000 and grows 6% each year. complete parts (a) through (e).
a) the initial amount a is 15000.
b) the percent rate of change is 6%, so the growth factor b is 1 + 0.06 = 1.06.
c) to find the number of students enrolled after one year, you calculate 15,000 • □.

Explanation:

Step1: Identify the growth factor

From part (b), we know the growth factor \( b = 1.06 \) (since the growth rate is 6%, so \( b=1 + 0.06=1.06 \)).

Step2: Calculate the number of students after one year

The formula for exponential growth is \( y=a\times b^{t} \), where \( a \) is the initial amount, \( b \) is the growth factor, and \( t \) is the time in years. Here, \( a = 15000 \), \( b = 1.06 \), and \( t = 1 \). So we need to calculate \( 15000\times1.06^{1} \), which is \( 15000\times1.06 \).

Step3: Perform the multiplication

\( 15000\times1.06=15000\times(1 + 0.06)=15000\times1+15000\times0.06 = 15000+900=15900 \)

Answer:

\( 1.06 \) (and the number of students after one year is \( 15900 \))

(Note: For part (c), the blank should be filled with the growth factor \( 1.06 \) as we use the formula \( \text{Final Amount}=\text{Initial Amount}\times\text{Growth Factor} \) for \( t = 1 \) year. So the calculation is \( 15000\times1.06 \))