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PilotLPTM [1.2K]
3 years ago
10

Write an exponential equation in the form y = ab* whose graph passes through points (2, 18) and (5, 60.75).

Mathematics
1 answer:
DochEvi [55]3 years ago
8 0

Let y=ab^x, as described in the problem statement. Plugging in x=2 and x=5 gives us the equations 18=ab^2 and 60.75=ab^5. Since a,b are nonzero, we divide the second equation by the first to get \frac{27}{8}=b^3, which means that b=\frac{3}{2}, after taking the cube root. Plugging this value for b into the first equation, we now have 18=a(3/2)^2=\frac{9a}{4}. Solving gives a=8, and our desired exponential equation is \boxed{y=8\left(\frac{3}{2}\right)^x}.

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