Determine if the table shows a linear or an exponential function

The table shows an exponential function

Step-by-step explanation:

Linear vs Exponential Functions

A linear function is written as:

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

An exponential function is written as:

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

Calculate the slope for (0,4) and (1,2):

Calculate the slope for (1,2) and (2,1):

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

The radical of index 1 is simply equal to its argument:

Now calculate the ratio for (0,4) and (2,1)

Testing other points we'll find the same ratio, thus the table is an exponential function

19

step-by-step explanation:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!