The first year of charity walk event had an attendance of 500. The attendance y increase by 5% each year. Write an exponential growth function to represent this situation. How many people will attend in the 10th year? Round your answer to the nearest person.

In the 10th year, there were 776 people in attendance.

An exponential growth function is given by:

y = abˣ

where y,x are variables, a is the initial value of y and b is the multiplier.

Given that the first year had an attendance of 500, hence a = 500. Also, there is an increase of 5% each year, hence b = 5% + 100% = 1.05

Therefore the exponential function is given by:

Hence in the 10th year, there were 776 people in attendance.

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Step-by-step explanation:

An exponential function has a standard form of

where a is the initial value and b is the growth/decay rate in decimal form.

If the walk had an attendance of 500 the first year, that means that for us,

a = 500

If the attendance is expected to increase by 5% each year, then not only does b retain its initial attendance, it is added to by 5%: 100% + 5% = 105% or, in decimal form, 1.05

Our function, then, is

and we need to solve for the number of people, y, that will attend in year x = 10:

First raise 1.05 to the 10th power to get

y = 500(1.628894627) and then multiply those 2 numbers together to get

y = 814.4 or 814 people in the 10th year

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