Question

Which ordered pairs lie on the graph of the exponential equation

Answer 1

`f(x)=25(2.2)^x`

One way to solve this is to fit the choices into the function

Let's take choice no.3 to illustrate how it is done.

(1 , 55)

Meaning if x = 1 , f(x) must be 55.

`\begin{gathered} f(x)=25(2.2)^x \\ f(x)=25(2.2)^1 \\ f(x)=25(1) \\ f(x)=25 \end{gathered}`

so if x = 1, then f (x) is 25. Therefore, choice number 3 is NOT the answer.

Let's take choice no. 2.

(0.5, 37.08)

Meaning if we substitute 0.5 in x, we have to get 37.08 as the value of f(x).

Let's see.

`\begin{gathered} f(x)=25(2.2)^x \\ f(x)=25(2.2)^(0.5) \\ f(x)=25(1.4832) \\ f(x)=37.08 \end{gathered}`

If x = 0.5, f(x) = 37.08. Therefore choice 2 is a CORRECT answer

Let's try the other choices , to checkif there are more than one correct answer

Let's take choice no.1

( 0.0)

`\begin{gathered} f(x)=25(2.2)^x \\ f(x)=25(2.2)^0 \\ f(x)=25(1) \\ f(x)=25 \end{gathered}`

choice number 1 is NOT the answer.

Lastly, choice n0.4

(2,121)

`\begin{gathered} f(x)=25(2.2)^x \\ f(x)=25(2.2)^2 \\ f(x)=25(4.84) \\ f(x)=121 \end{gathered}`

If x = 2, f(x) = 121. Therefore choice 4 is a CORRECT answer

Answers:

Choice 2 (0.5, 37.08)

Choice 4 (2, 121)