Beth's mother was upset with her because Beth's text messages from the previous month were 218% of the amount that their data plan allowed without incurring an extra charge. Beth's mother had to pay extra money for each text message over the allowance. Beth had 5,450 text messages last month. How many text messages is Beth allowed under her data plan with no extra cost?

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.