Question

which of the following exponential function me goes through the points (1,20) and (2,80)

Answer 1

Answer:

$f(x)=5(4^x)$

Step-by-step explanation:

Let $y=ab^x$ be the equation of the exponential function.

This exponential function goes through (1,20).

We put x=1 and y=20 into the above equation to get:

$20=ab^1$

$20=ab$.....eqn (`1)

 This exponential function again goes through (2,80).

We put x=2 and y=80 into the above equation to get:

$80=ab^2$.....eqn (`2)

Divide equation (2) by equation (1)

$\frac{80}{20}=\frac{ab^2}{ab}$

$\implies 4=b$

Put b=4 in equation 1.

$20=4a$

$\implies a=5$

The required exponential function is $y=5(4^x)$ or  $f(x)=5(4^x)$