Question

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

Answer 1

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
`(27)/(8)=b^3,` which means that
`b=(3)/(2),` after taking the cube root. Plugging this value for
`b` into the first equation, we now have
`18=a(3/2)^2=(9a)/(4).` Solving gives
`a=8,` and our desired exponential equation is
`\boxed{y=8\left((3)/(2)\right)^x}.`