Rip-Off Rentals charges $25 per day plus 50¢ per mile to rent a mid-sized car. Your teacher will rent you his or her family sedan and charge you only 3¢ if you drive one mile, 6¢ if you drive two miles, 12¢ if you drive three, 24¢ for four, and so on. Homework Help ✎ Write an equation that will give you the cost to rent each car.

Don't rent your teacher's car; that's just asking for trouble.  And teachers, don't rent cars to students.

Let d be the number of days the car is rented for and m the number of miles it was driven while rented.

R.O.R. car costs in $:

R = 25d + 0.50m

Teacher car costs in $:

T = 0.03 · 2^m

where the caret ^ of course means exponentiation.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2