College Enrollment The number of students enrolled at a...

College Enrollment The number of students enrolled at a college is 15, 000 and grows $4\%$ each year. a. The initial amount $a$ is b. The percent rate of change is $4 \%$, so the growth factor $b$ is $1+=$. c. To find the number of students enrolled after one year, you calculate $15,000$. d. Complete the equation $y= \cdot$ to find the number of students enrolled after x years. e. Use your equation to predict the number of students enrolled after 25 yr.

College Enrollment The number of students enrolled at a college is 15, 000 and grows $4\%$ each year.
a. The initial amount $a$ is
b. The percent rate of change is $4 \%$, so the growth factor $b$ is $1+=$.
c. To find the number of students enrolled after one year, you calculate $15,000$.
d. Complete the equation $y= \cdot$ to find the number of students enrolled after x years.
e. Use your equation to predict the number of students enrolled after 25 yr.

Key Concepts

Exponential Growth

Exponential growth describes a process where a quantity increases by a constant proportion in each equal time interval. This characteristic makes it particularly useful for modeling situations where a population or investment grows at a fixed percentage rate over time.

Initial Value

The initial value is the starting amount before any growth has occurred. In the context of exponential growth models, it provides the baseline quantity from which all future growth is computed.

Growth Factor

The growth factor is the multiplier that is applied to the initial value each period to account for the percentage change. It is calculated by adding one to the growth rate expressed as a decimal, reflecting how the quantity changes with each time interval.

Exponential Function

An exponential function is used to model scenarios of exponential growth. It takes the form y = a * b^x, where 'a' represents the initial value, 'b' represents the growth factor, and 'x' is the number of time periods. This function can be used to predict future outcomes based on the rate of change.

Rate of Change (Percent Increase)

The percent rate of change provides the percentage increase per time period and is crucial for determining the growth factor. A growth of 4% per year, for instance, is incorporated into the model by converting it to its decimal form and adding one, forming the basis of the growth multiplier.

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