Question

The table represents some points on the graph of an exponential functio
X
f(x)
2
36
3
54
4
81
5
121.5
6
182.25
Which function represents this relationship?
F f(x) = 16
Nw
G f(x) =
= 16
Nm
H f(x) = 36
ਹੈ।
f(x) = 36
WIN

Answer 1

The exponential function represented in the table is given by:

$F(x) = 16\left(\frac{3}{2}\right)^x$, which means that option F is correct.

What is an exponential function?

It is modeled by:

$y = ab^x$

In which:

• a is the initial value.

• b is the rate of change.

Considering the table, that has points (2,36) and (3,54), we have that:

$36 = ab^2$

$a = \frac{36}{b^2}$

$54 = ab^3$

$54 = \frac{36}{b^2} \times b^3$

$36b = 54$

$b = \frac{3}{2}$

Hence:

$y = a\left(\frac{3}{2}\right)^x$

When x = 2, y = 36, hence:

$y = a\left(\frac{3}{2}\right)^x$

$36 = a\left(\frac{3}{2}\right)^2$

$\frac{9}{4}a = 36$

$a = 16$

Hence, the function is:

$F(x) = 16\left(\frac{3}{2}\right)^x$, which means that option F is correct.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer 2

Answer:

option F

Step-by-step explanation:

F(x)=16(3/2)^x