Question

The graph of an exponential model in the form y = a ⋅ bx passes through the points (2, 50) and (3, 250). Which point is also on the graph?

A. (0, 5) B. (1, 10) C. (4, 450) D. (5, 650)

Answer 1

We choose B. (1, 10)

Explanation:

Given the exponential model in the form y = a
`b^(x)`

• passes through the points (2, 50)

<=> 50 = a
`b^(2)`

<=> a =
`(50)/(b^(2) )` (1)

• passes through the points (3, 250)

<=> 250 = a
`b^(3)` (2)

Substitute (1) into (2) we have:

250 =
`(50)/(b^(2) )`
`b^(3)`

<=> 50b = 250

<=> b = 5

=> a =
`(50)/(5^(2) )` = 2

Hence, our exponential model is: y =2*
`5^(x)`

Let analyse all possible answer:

A. (0, 5) we have: y =2*
`5^(0) =2` ≠ 5 so it is wrong

B. (1, 10) we have: y = 2*
`5^(1) =10` so it is true

C. (4, 450) we have: y = 2*
`5^(4) =1250` ≠ 450 so it is wrong

D. (5, 650) we have: y = 2*
`5^(5) =6250` ≠ 650 so it is wrong

Hence we choose B. (1, 10)