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Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
The points are given as:
(3,6.5) and (4,17.55)
An exponential equation is represented as:
[tex]y = ab^x[/tex]
Using the given points, we have the following equations:
[tex]ab^3 = 6.5[/tex]
[tex]ab^4 = 17.55[/tex]
Divide both equations:
[tex]ab^4 \div ab^3 = 17.55 \div 6.5[/tex]
Evaluate
b = 2.7
Substitute b = 2.7 in [tex]ab^3 = 6.5[/tex]
[tex]a * 2.7^3 = 6.5[/tex]
Solve for a
[tex]a = \frac{6.5}{2.7^3}[/tex]
Substitute [tex]a = \frac{6.5}{2.7^3}[/tex] and b = 2.7 in [tex]y = ab^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
His point (5,28.6) means that:
x = 5 when y = 28.6
Substitute x = 5 in [tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^5[/tex]
Evaluate
y = 47.385
y = 47.385 and y = 28.6 are not the same
Hence, Mike's claim is incorrect
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