Question

What is the exponential function modeled by the following table? x f(x) 3 8 4 16 5 32 (1 point) f(x) = 2x f(x) = x2 f(x) = x3 f(x) = 3x

Answer 1

Answer:

First option is correct.

Step-by-step explanation:

From the given table it is noticed that the exponential function passing through (3,8), (4,16) and (5,32).

Let the exponential function be

$f(x)=ab^x$

The exponential function passing through (3,8).

$8=ab^3$      ..... (1)

The exponential function passing through (4,16).

$16=ab^4$  ..... (2)

Divide equation 2 by equation 1.

$2=b$

Put this value in equation 1.

$8=a(2)^3$

$8=8a$

$a=1$

The value of a is 1 and the value of b is 2, therefore the function is defined as

$f(x)=2^x$

Therefore first option is correct.

Answer 2

The first answer choice, f(x)=2^x

ex: 2^3= 2*2*2=8