Unit 6 Algebra 2

Question

The graph of an exponential model in the form y=a*b^x passes through the points (1, 12) and (2, 48). Which point is also located on the graph?

Answer 1

We can start by creating a chart:

1 12

2 48

In exponential functions, the first column of the chart will increase by 1 and the second column will increase by a factor. To figure out what that factor is, we can do 48/12 = 4. In other words, when x increases by 1, y is multiplied by 4. This is our b value.

Add a row with x=0 to the chart:

0 3

1 12

2 48

When x = 0, the corresponding y-value will be the a-value in the equation. So the a-value is 3.

Now that we know a and b, we can write the equation.

y = a•b^x

y = 3•4^x

Any point that makes this equality true will be located on the graph of the function. For example, we can test the points (4, 100) and (4, 192).

Using (4, 100):

100 = 3•4⁴

100 = 3•64

100 = 192

Since this is false (100 does not actually equal 192), the point (4, 100) is not on the graph.

Using (4, 192):

192 = 3•4⁴

192 = 3•64

192 = 192

Since this is true (192 is equal to 192), the point (4, 192) is on the graph.

Answer 2

Hi,

y=a*b^x passes through the points (1, 12) and (2, 48). Which point is also located on the graph?

First, plug in given information in function it means:

(1, 12) -------> 12 = a * b ¹------> 12 = ab

(2, 48) -------> 48 = a * b² -------> you can write b* b instead b² so you have 48 = a *b * b, on the other hand you have 12 = a*b Now you plug in 48 = a *b * b = 12 * b after solving this equation 48 = 12 * b ,

b = 4

one more time use 12 = a*b by plug in b = 4 then you have 12 = a * 4 ====> a = 3

by doing that you found an exponential function y = 3 * 4 ^x

if you need to find other points on this function you choose any x then find y

example: x = 0 ----> y = 3

x = 3 -----> y = 192

x = 4 -----> y = 768 AND SO ON

I hope it is useful,

Minoo