Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$T. 3 Write exponential functions: word problems DBW. Lakewood Children's Theater started a summer program last year with 245 students. Thanks to some advertising during the off-season, 294 students have enrolled this year. The theater will continue this advertising strategy in hopes that enrollment will continue to increase. Write an exponential equation in the form y=a(b)^(x) that can model the number of enrolled students, y,x years after the program began. Use whole numbers, decimals, or simplified fractions for the values of a and b. y=$

T. $3$ Write exponential functions: word problems DBW. $\newline$ Lakewood Children's Theater started a summer program last year with $245$ students. Thanks to some advertising during the off-season, $294$ students have enrolled this year. The theater will continue this advertising strategy in hopes that enrollment will continue to increase. $\newline$ Write an exponential equation in the form $y=a(b)^{x}$ that can model the number of enrolled students, $y, x$ years after the program began. $\newline$ Use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$ . $\newline$ $y=$

View step-by-step help

Home

Math Problems

Algebra 1

Write exponential functions: word problems

Full solution

Q. T.

3

Write exponential functions: word problems DBW.

\newline

Lakewood Children's Theater started a summer program last year with

245

students. Thanks to some advertising during the off-season,

294

students have enrolled this year. The theater will continue this advertising strategy in hopes that enrollment will continue to increase.

\newline

Write an exponential equation in the form

y=a(b)^{x}

that can model the number of enrolled students,

y, x

years after the program began.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

and

b

\newline

y=

Rephrase Question: First, let's rephrase the ＂What is the exponential equation that models the number of enrolled students in the Lakewood Children's Theater summer program, $y$ , $x$ years after the program began?＂
Identify Initial Value and Growth Rate: Identify the initial value $a$ and the growth rate $r$ . The initial value $a$ is the number of students when the program began, which is $245$ . To find the growth rate $r$ , we need to calculate the rate of increase from the first year to the second year.
Calculate Growth Rate: Calculate the growth rate $r$ . The number of students increased from $245$ to $294$ in one year. To find the growth rate, we use the formula: $r = \left(\frac{\text{final amount}}{\text{initial amount}}\right) - 1$ $r = \left(\frac{294}{245}\right) - 1$ $r = 1.2 - 1$ $r = 0.2$ The growth rate $r$ is $0.2$ , which means there is a $20\%$ increase per year.
Determine Growth Factor: Determine the growth factor $b$ . The growth factor $b$ is $1$ plus the growth rate $r$ , so: $b = 1 + r$ $b = 1 + 0.2$ $b = 1.2$
Write Exponential Equation: Write the exponential equation in the form $y = a(b)^x$ . We have the initial value ( $a$ ) as $245$ and the growth factor ( $b$ ) as $1.2$ . The exponential equation is: $y = 245(1.2)^x$