Question

write the equation for an exponential function, in the form y=a*b^2, whose graph passes through the coordinate points (1,7.5) and (3,16.875)

Answer 1

To find the equation of the exponential function, we can use the two coordinate points given:

(1, 7.5) --> y = a * b^1
(3, 16.875) --> y = a * b^3

Using the first point:
7.5 = a * b

Using the second point:
16.875 = a * b^3

We can divide the second equation by the first equation to eliminate 'a':
16.875 / 7.5 = b^3 / b
2.25 = b^2

Now that we have found the value of 'b', we can substitute it back into the first equation to find the value of 'a':
7.5 = a * 2.25
a = 7.5 / 2.25
a = 3.33333333

Therefore, the equation of the exponential function passing through the given points is:

y = 3.33333333 * 2.25^x