Company A is offering $10,000 for the first month and will increase the amount each month by $5,000 Company B is offering $500 for the first month and will double their payment each month. For which monthly payment will Company B’s payment first exceed Company A’s payment? Round your answer to the nearest whole month. Prove your answer is correct.

8 months

Step-by-step explanation:

Let's do the check( we are checking if it's the correct formula with the table we provided)  Company A's payment, month n: 10000 + 5000(n-1)  since n = 8:  A :10000 + 5000*7 = 45000 Company B's payment, month n: 500 * 2^(n-1) since n = 8: 500 * 2^7 = 64000 When is [A] = : 10000 + 5000(n-1) = 500 * 2^(n-1) Simplify to get: 10(n-1) - 2^(n-1) + 20 = 0 = 10n - 10 - 2^(n-1) + 20= 0 10n - 2^(n - 1) = -10 If we solve for n we have N= 7.39 months which is 8 months  Lets assume that mth is months ca is company A and cb is company B  MTH      CA           CB   1      10,000        500   2      15,000      1,000   3      20,000      2,000   4      25,000      4,000   5      30,000      8,000   6      35,000     16,000   7      40,000     32,000   8      45,000     64,000

With a continuous thought process.