Which of the following exponential functions goes through the points (1, 6) and (2, 12)?
f(x) = 3(2)^x
f(x) = 2(3)^x
f(x) = 3(2)^-x
f(x) = 2(3)^-x

Solution:

Given, the points are (1, 6) and (2, 12).

We have to find the exponential function that goes through the given points.

From the option,

a) f(x) = 3(2)^x

Put x = 1,

f(1) = 3(2)¹

= 3(2)

= 6

Put x = 2,

f(2) = 3(2)²

= 3(4)

= 12

Therefore, the exponential function f(x) = 3(2)^x goes through the given points.

b) f(x) = 2(3)^x

Put x = 1,

f(1) = 2(3)¹

= 2(3)

= 6

Put x = 2,

f(2) = 2(3)²

= 2(9)

= 18

Therefore, the exponential function f(x) = 2(3)^x does not go through the given points.

c) f(x) = 3(2)^-x

Put x = 1,

f(1) = 3(2)^-1

= 3/2

Put x = 2,

f(2) = 3(2)^⁻2

= 3/4

Therefore, the exponential function f(x) = 3(2)⁻x does not go through the given points.

d) f(x) = 2(3)^-x

Put x = 1,

f(1) = 2(3)^-1

= 2/3

Put x = 2,

f(2) = 2(3)^-2

= 2/9

Hence, the exponential function f(x) = 2(3)^x does not go through the given points.

Therefore, the exponential function  f(x) = 3(2)^x goes through the points.

---

Which of the following exponential functions goes through the points (1, 6) and (2, 12)?

Summary:

The exponential function  f(x) = 3(2)^x goes through the points (1, 6) and (2, 12).