SOLUTION: The amount A of money on deposit for t years in an account earning simple interest is a linear function of t. Express that function as an equation if A = $173 when t = 5 and A = $2

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Question 126: The amount A of money on deposit for t years in an account earning simple interest is a linear function of t. Express that function as an equation if A = $173 when t = 5 and A = $233 when t = 8.



Found 2 solutions by KMST, ikleyn:
Answer by KMST(5484) About Me  (Show Source):
You can put this solution on YOUR website!
We start with A=at%2Bb

A linear function is a function of the form y=ax%2Bb or f%28x%29=ax%2Bb .
If we graph a linear function, the graph is a straight line.
In this case, the variable of the function is called t rather than x ,
and the value of the function is called A instead of y or f%28x%29 ,
so we write the function as A=at%2Bb .

A = $173 when t = 5, so we replace 173 for A and 5 for t , and get 173=a%2A5%2Bb or as usually written 5a%2Bb=173 .
A = $233 when t = 8, so we replace 233 for A and 8 for t , and get 233=a%2A8%2Bb or as usually written 8a%2Bb=233 .

Now we have to solve the system of equations system%285a%2Bb=173%2C8a%2Bb=233%29
to find the values of a and b .

One way to do it:
system%285a%2Bb=173%2C8a%2Bb=233%29 --> system%28b=173-5a%2C8a%2Bb=233%29 --> system%28b=173-54%2C8a%2B173-5a=233%29 --> system%28b=173-54%2C8a-5a=233-173%29 --> system%28b=173-5a%2C3a=60%29 --> system%28b=173-5a%2Ca=60%2F3%29 --> system%28b=173-5a%2Ca=20%29 --> system%28b=173-5%2A20%2Ca=20%29 --> system%28b=173-100%2Ca=20%29--> highlight%28system%28b=73%2Ca=20%29%29

Our function seems to be A=20t%2B73 .
Let's check, to verify that I did not make any mistake.
For t=5 , the function says A=20%2A5%2B73 --> A=100%2B73 --> A=173 .
For t=8 , the function says A=20%2A8%2B73 --> A=160%2B73 --> A=233 .

Answer by ikleyn(54060) About Me  (Show Source):
You can put this solution on YOUR website!
.
The amount A of money on deposit for t years in an account earning simple interest is a linear function of t.
Express that function as an equation if A = $173 when t = 5 and A = $233 when t = 8.
~~~~~~~~~~~~~~~~~~~~~~~~~~~


        You can solve this problem mentally, without using equations. 


In three years, from t = 5 to t = 8, the amount A increases by 233 - 173 = 60 dollars.


Hence, the growth rate is 60/3 = 20 dollars per year.


Thus, since the amount was 173 dollars at t = 5 years, it was 173 - 5*200 = 173 - 100 = 73 at the beginning (when t = 0).


So, the function expression for A is A = 73 + 20t for t >= 0.    ANSWER

Solved mentally.