Please help with this problem.

Question

 

1) you want to write a function, f(x), to represent the money in an inheritance account. every year since the account was started (it was started in 2005) the person has withdrawn the maximum yearly withdrawal of $15,000. in the year 2015 the account now had $210,000. answer the following questions: a) write a linear function (using function notation) that represents the amount of money in the account x years since 2005. show work.

 

 

 

b) How much money was originally in the account? SHOW WORK USING THE FUNCTION.
c) How much money will be in the account in the year 2025? SHOW WORK USING THE FUNCTION.
d) In what year (to the nearest year) will the account run out of money? SHOW WORK USING THE FUNCTION.

Answer 1

I would start this problem by listing what is known and what is unknown in the problem.

 

Known: This is information given in the problem

in 2015 there is $210,000 in the account

every year the account is decreased by $15,000

the account was started in 2005

x is the number of years since 2005

 

Unknown: These will be variables or things we are trying to find in the problem

the starting amount in the account (call this the variable s)

the current amount of money in the account (we want this to be the output of the function so call it f(x))

 

a) If we knew the starting amount, this would be simple. We would just be subtracting the amount that has been taken out of the account from the starting amount to get.

F(x) = s - 15,000(x)

 

However, we don't know the starting amount. We do know the amount in 2015 though. We can adjust the function using this information. We will pretend that the account is starting in 2015, and so the value of s becomes 210,000. However, we can't just leave x, we have to adjust it as well. Since 2015 is 10 years after 2005, the adjusted x will be x-10. We have to subtract 10 to get from 2015 back to the real starting year of 2005.

F(x) = 210,000 - 15,000(x-10)

 

b) The original amount will be the amount in the account when x = 0. Plug 0 in for x and solve for F(0).

F(0) = 210,000 - 15,000(0-10)

 

c) The amount in the account in 2025 will be the amount 20 years after 2005 or when x = 20. Plug 20 in for x and solve for F(20).

F(20) = 210,000 - 15,000(20-10)

 

d) The account will be out of money when the function gives a value of 0. Plug 0 in for F(x) and solve for x.

0 = 210,000 - 15,000(x-10)