Question

Bear Mountain Summer Camp opened last year and had 650 campers. After doing some advertising in the off-season, the camp has enrolled 676 campers for this year, and enrollment is expected to continue increasing each year. Write an exponential equation in the form y = a(b) that can model the number of campers, y, x years after the camp opened. Use whole numbers, decimals, or simplified fractions for the values of a and b.​

Answer 1

y = 650(1.04^x)

Explanation:

You want an exponential equation that models the increase of campers from 650 to 676 in one year, continuing at the same rate of growth.

Exponential function

Your function is to be of the form ...

y = a(b^x)

In this form, 'a' is the initial value, 650. The parameter 'b' is the growth factor per year, which is 676/650 = 26/25 = 1.04.

Using the decimal value for 'b', the exponential equation is ...

y = 650(1.04^x)

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Additional comment

As a reduced fraction, the value of 'b' could be 26/25. The decimal form is more compact and has the same accuracy.

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