Question

Which of the following exponential functions goes through the points (1, 12) and (2, 36)?

a
f(x) = 4(3)−x

b
f(x) = 3(4)−x

c
f(x) = 3(4)x

d
f(x) = 4(3)x

Answer 1

The function through which given point passes is f(x) = 24 x - 12 .

Explanation:

Given as :

The points are

`x_1` ,
`y_1` = 1 , 12

`x_2` ,
`y_2` = 2 , 36

now, slope of the line

Let The slope of line = m =
`(y_2-y_1)/(x_2-x_1)`

Or, m =
`(36 - 12)/(2-1)`

Or, m = 24

So The slope of line = m = 24

Now, equation of line in point-slope form

y -
`y_1` = m × (x -
`x_1` )

Or, y - 12 = 24 × (x - 1 )

or, y - 12 = 24 x - 24

or, y = 24 x - 24 + 12

or, y = 24 x - 12

or , f(x) = 24 x - 12

So, The function through which given point passes is f(x) = 24 x - 12 . Answer