Answer:
Step-by-step explanation:
An exponential function has a standard form of
[tex]y=a(b)^x[/tex] 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
[tex]y=500(1.05)^x[/tex] and we need to solve for the number of people, y, that will attend in year x = 10:
[tex]y=500(1.05)^{10}[/tex]
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
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:
[tex]y = 500(1.05)^{x-1}\\\\In\ the\ 10th\ year:\\y = 500(1.05)^{10-1}=776[/tex]
Hence in the 10th year, there were 776 people in attendance.
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