could anyone please help me with this?

Question

Twin brothers, Collin and Cameron, get jobs immediately after graduating from college at the age of 22. Collin opts for the higher starting salary, $55,000, and stays with the same company until he retires at 65. His salary doubles every 15 years. Cameron opts for a lower starting salary, $35,000, but moves to a new job every 5 years; he doubles his salary every 10 years until he retires at 65. What is the annual salary of each brother upon retirement?

Answer 1

The exponential doubling formula is:

 

S(t) = S₀·2^t/a

 

where:

• S(t) = salary at year t
• S₀ = the starting salary ($55,000 for Collin, $35,000 for Cameron)
• t = time = 65 - 22 = 43 years at retirement
• a = the doubling period (15 years for Collin, 10 years for Cameron)

 

For Collin at retirement (age 65):

 

S(t) = $55,000·2^43/15 = ____?

 

Use your calculator to compute the answer.

 

For Cameron:

 

S(t) = $35,000·2^43/10 = ____?

 

Again, use your calculator to get the answer.

Answer 2

Collin's salary doubles every 15 years and will double at age 37 and 52.

 

He will be making $110,000 at age 37 . He will be making $220,000 at age 52 and at retirement.

 

Cameron's salary double every 10 years and will double at age 32, 42, 52 and 62

 

He will be making $70,000 at age 32, $140,000 at age 42, He will be making $280,000 at age 52, and $560,000 at 62

 

and retirement.