Alicia has invented a new app that two companies are interested in purchasing for a 2-year contract. Company \text{A}Astart text, A, end text is offering \$10{,}000$10,000dollar sign, 10, comma, 000 for the first month and will increase the amount each following month by \$5000$5000dollar sign, 5000. Company \text{B}Bstart text, B, end text is offering \$500$500dollar sign, 500 for the first month and will double their payment each following month. For which monthly payment will Company \text{B}Bstart text, B, end text's payment first exceed Company \text{A}Astart text, A, end text's payment?

8th Month

Step-by-step explanation:

For Company A

Company's A payment increases by a certain amount, it is therefore an Arithmetic Growth.

The nth term for an arithmetic progression is given by:

First term, a=$10,000; Common Difference,d=$5000

For Company B

Company's B payment doubles every month, it is therefore a Geometric Growth.

The nth term for an geometric progression is given by:

First term, a=$500; Common Ratio,r=2

We want to determine at which month, n Company B's Monthly Payment will exceed that of company A.

Using the nth term formula derived above:

In the 8th Month, the payment of Company B will exceed that of company A.