Plz ! thirty points for answering!
lakita has 65 water bottles for the 5k race participants. in addition, she is planning to buy some boxes of water bottles that have 16 water bottles each. all of the boxes cost the same. lakita is not sure yet about the number of boxes of water bottles she wants to buy, but she has enough money to buy up to 5 of them. write a function rule to describe how many water bottles lakita can buy. let x represents the number of boxes of water bottles lakita buys. find a reasonable range for the function.
a) f(x) = 65x + 16
{81, 97, 113, 129, 145}
b) f(x) = 65x + 16
{145}
c) f(x) = 16x + 65
{65, 81, 97, 113, 129, 145}

If Lakita buys x boxes of water bottles, she will have y = 16x + 69 water bottles.

Lakita has enough money to buy only up to 5 boxes of water bottles, so she can buy 0, 1, 2, 3, 4, or 5 boxes of water bottles. These are the only reasonable values for the domain. Substitute these values into the function rule to find the range values.

f(x) = 16x + 65

{65, 81, 97, 113, 129, 145}

Step-by-step explanation:

Identify the independent and dependent variable.

Independent variable: x = number of boxes of water bottles Lakita buys

Dependent variable: f(x) = the total number of water bottles

Write the function rule.

f(x) 16x + 65         Add 65 water bottles to 16 times the number of boxes Lakita buys to get the total number of water bottles.

Identify reasonable domain values.

0, 1, 2, 3, 4, 5  The domain is the number of boxes of water bottles Lakita can buy.

Calculate f(x) for each value of x.

f (0) = 16(0) + 65 = 65

f (1) = 16(1) + 65 = 81

f (2) = 16(2) + 65 = 97

f (3) = 16(3) + 65 = 113

f (4) = 16(4) + 65 = 129

f (5) = 16(5) + 65 = 145

A reasonable range for the function is {65, 81, 97, 113, 129, 145}.

There is an exponent rule(a^b)^c = a^(b * c)

so (153^2)^7 = 153^(2 * 7) = 153^14