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

Answer:

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

Step-by-step 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 = $\frac{y_2-y_1}{x_2-x_1}$

Or, m = $\frac{36 - 12}{2-1}$

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