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

Answer:

We choose B. (1, 10)

Step-by-step explanation:

Given the exponential model in the form y = a$b^{x}$

• passes through the points (2, 50)

<=> 50 = a$b^{2}$  

<=> a = $\frac{50}{b^{2} }$ (1)

• passes through the points  (3, 250)

<=> 250 = a$b^{3}$ (2)

Substitute (1) into (2) we have:

250 =  $\frac{50}{b^{2} }$$b^{3}$

<=> 50b = 250

<=> b = 5

=> a = $\frac{50}{5^{2} }$ = 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)