Question

х
f(x
Which exponential function is represented by the
values in the table?
-2
AW
-1
3
2
O 3
f(x) = 3(2)
O f(x) = 2(2)
O f(x) = 3(34)
O f(x) = 2(3)
0
3
1
6
1
2
2
12

Answer 1

Answer:

$y = 3(2)^x$

Step-by-step explanation:

Given

The attached table

Required

Determine the exponential function

An exponential function is represented as:

$y = ab^x$

From the table;

$(x,y)=(0,3)$

So:

$y = ab^x$

$3 = a * b^0$

$3 = a * 1$

$3 = a$

$a = 3$

Also:

$(x,y) = (1,6)$

So:

$y = ab^x$

$6 = a * b^1$

$6 = a * b$

Substitute $a = 3$

$6 = 3 * b$

Solve for b

$b = 2$

So:

$y = ab^x$

$y = 3(2)^x$

Answer 2

The exponential function represented by the values is f(x) = 3(2)ˣ

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

From the table, at point (0, 3):

3 = ab°  

a = 3

At point (2, 12):

12 = ab²

12 = 3b²

b² = 4

b = 2

f(x) = 3(2)ˣ

The exponential function represented by the values is f(x) = 3(2)ˣ

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