Question

Which equation of an exponential function has a graph that passes through the points

(1,5) and (2,15)?

Answer 1

`y = (5)/(3) (3^(x) )`

Explanation:

In general,
`y = k(b^(x))`

Substitute x = 2, y = 15

(1)
`15 = kb^(2)`

Substitute x = 1, y = 5

(2)
`5 = kb^(1) = kb`

Divide equation (1) by equation (2)

`(15 = kb^(2) )/(5= kb )`

3 = b

Now substitute b = 3 in equation (2) to find k

5 = k(3)

`k = (5)/(3)`

Since we know the values for k and b, we now have the exponential function that passes thru (1, 5) and (2, 15)

`y = (5)/(3) (3^(x) )`