Question

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

Answer 1

Answer:

The values of a and b are:

• a = 2

• $b=4$

Step-by-step 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

$2b^3=128$

$\frac{2b^3}{2}=\frac{128}{2}$

$b^3=64$

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

• $b=4$