Question

Which exponential function is represented by the graph?

Answer 1

see explanation

Explanation:

The exponential function is in the form

y = a
`(b)^(x)`

Use points on the graph to find a and b

Using (0, 3), then

3 = a
`(b)^(0)` ⇒ a = 3

Using (1, 6), then

6 = 3
`(b)^(1)` ⇒ b = 6 ÷ 3 = 2

The equation is y = 3
`(2)^(x)`

Answer 2

y =
`3*2^(x)`

Explanation:

The general form for an exponential function is :

y =
`ab^(x)`

We need to find out what a and b are using the values given in the graph.

we can see that (x=0, y = 3) and (x=1, y = 6) are points on the curve. Substitute these into the general equation

for (x=0, y = 3),

3 =
`ab^(0)`

3 = a (1) or a = 3

for (x=1, y = 6),

6 =
`ab^(1)`

6 = ab (substitute a=3 from previous calculation)

6 = 3b

b = 2

Hence the equation is:

y =
`3*2^(x)`

Edit reason: typo in the final answer