Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $28 monthly fee and charges an additional $0.09 for each minute of calls. The second plan has no monthly fee but charges $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

700 Minutes

Step-by-step explanation:

For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.

For the first phone plan, we have a base $28 and additional $0.09 per minute of call.  This can be expressed as:

28 + 0.09x                  Where x is the number of minutes used

For the second phone plan, we have a flat $0.13 per minute of call.  This can be expressed as:

0.13x                           Where x is the number of minutes used

To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.

28 + 0.09x = 0.13x

28 + 0.09x + -0.09x = 0.13x + -0.09x

28 = 0.04x

28 = (1/25)x

28 * 25 = (1/25)x * 25

28 * 25 = x

700 = x

Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.

Cheers.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)