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=

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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 = (final amount / initial amount) - 1 r = (294 / 245) - 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 = 1.2Write 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

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