Part 4 of 5

The number of students enrolled at a college is 17,000 and grows each year. Complete parts (a) through (e)
a) The initial amount a is 17,000
b) The percent rate of change is , so the growth factor is .
c) To find the number of students enrolled after one year, you calculate 17,000 • 1.03.
d) Complete the equation - to find the number of students enrolled after years.

Ask by John Harper. in the United States

Jan 24,2025

Question

Part 4 of 5

The number of students enrolled at a college is 17,000 and grows each year. Complete parts (a) through (e)
a) The initial amount a is 17,000
b) The percent rate of change is , so the growth factor is .
c) To find the number of students enrolled after one year, you calculate 17,000 • 1.03.
d) Complete the equation - to find the number of students enrolled after years.

Ask by John Harper. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To complete part **(d)**, we need to formulate an exponential growth equation that represents the number of students enrolled after $$ x $$ years.

Given:
- **Initial amount $$ a $$**: 17,000 students
- **Growth factor $$ b $$**: $$ 1.03 $$ (since the enrollment grows by $$ 3\% $$ each year)

The general form of an exponential growth equation is:

$$
y = a \times b^x
$$

Plugging in the known values:

$$
y = 17,000 \times (1.03)^x
$$

**So, the completed equation is:**

$$
y = 17,000 \times (1.03)^x
$$

This equation allows you to calculate the number of students enrolled after $$ x $$ years by substituting the value of $$ x $$ into the equation.

**Example:**
To find the number of students after 2 years:

$$
y = 17,000 \times (1.03)^2 \approx 17,000 \times 1.0609 = 18,036.3
$$

So, approximately **18,036** students will be enrolled after 2 years.
The completed equation is: $$ y = 17,000 \times (1.03)^x $$