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 • 1.06.
d) complete the equation y = \square • \square^{\square} to find the number of students enrolled after x years.

Explanation:

Step1: Identify the formula for exponential growth

The general formula for exponential growth is \( y = a \cdot b^x \), where \( a \) is the initial amount, \( b \) is the growth factor, and \( x \) is the time in years.

Step2: Substitute the known values

From part (a), we know \( a = 15000 \). From part (b), we know the growth factor \( b = 1.06 \). So substituting these values into the formula, we get \( y = 15000 \cdot 1.06^x \).

Answer:

\( y = \boldsymbol{15000} \cdot \boldsymbol{1.06}^{\boldsymbol{x}} \)