Question

What are the values of a and b?
a=
b=

Answer 1

The values of a and b are:

• a = 2

• 
  `b=4`

Explanation:

Given the exponential model

`y=a\cdot \:b^x`

Given the points

(0, 2) and (3, 128)

We know that the y-intercept of
`y=a\cdot \:b^x` is (0, a).

so

a = 2

putting x = 3, y = 128 and a = 2

`y=a\cdot \:b^x`

`128=2\cdot \:b^3`

Switching sides

`2b^3=128`

`(2b^3)/(2)=(128)/(2)`

`b^3=64`

Taking the real value such as:

`\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)}`

so

`b=\sqrt[3]{64}`

`b=\sqrt[3]{4^3}`

`b=4`

Therefore,

• a = 2

• 
  `b=4`