Given that L is a linear function, L (5) = 100 and L (9) = 150.
a. Determine the value of L (13)

L(13) = 200

Step-by-step explanation:

Linear function:

A linear function has the following format:

In which m is the slope(how much y changes when x changes by 1) and b is the y-intercept(value of y when x = 0).

Finding the slope:

L (5) = 100 and L (9) = 150.

The slope is given by the change in the output(L, which is equals to y in the general formula) divided by the change in the input(x).

Change in the output: 150 - 100 = 50

Change in the input: 9 - 5 = 4

Slope:

So

L (5) = 100

So , which means that when , and we use this to find b.

So

a. Determine the value of L (13)

L when . So

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logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.