A gym offers two options for membership plans. Option A includes a one-time fee of $121 and then costs $1 per day. Option B has no initiation fee but costs $12 per
day.
a) Write an equation for the cost of each option.
b) After how many days will the cost of the two options be the same? How
much will both options cost at that time?

Identify variables:
x= # of days
y= total $ amount

Equation:

121+1x=12x

subtract -1x on both sides:

121+1x=12x
-1x -1x

1x-1x cancels out and 12x-1x is 11x so new equation is:

121=11x

now divide 11 on both sides

121 divided by 11 is 11. 11 divided by 11 is 1.

x=11

Now plug x=11 in option A.

121+1(11)=y

121+11=y

132=y

Now plug x=11 to option B.

12(11)= y

132=y

After 11 days the cost of the two options will be the same and both options would cost $132.

Exponential function

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice