write an equation that result in the indicated translation. The absolute value function shifted 7 units to the left.

Question

1. write an equation that result in the indicated translation. The absolute value function shifted 7 units to the left.

 

2. The linear equation y=78.68x+1124 provides an approximation of the value(in dollar) of an account opened on January 1, 1988,in the amount of $1124and earing 7% simple interest, where x=0 represent January 1, 1988,x=1 represent January 1, 1989, x=2 represent January 1, 1990 and so on.

write an equation that yield the same y-value when the exact year number is ended. 

Answer 1

Hi Vivian,

 

In answer to your first question, the equation for shifting the absolute value function 7 units to the left is:  y = |x+7|

 

The sign before the number of units shifted is opposite to that of the actual shift.  Since shifting is 7 units to the left (negative shift along x-axis) then the function (equation) representing this shift is written with the opposite sign (+7).

 

For visual confirmation of this concept - click the link below to see the graphs (blue graph is original absolute function and red graph is the absolute function shifted 7 units to the left):

 

https://dl.dropbox.com/s/wwqge4ok7gtyk2f/Absolute_Value_Functions.png?raw=1

 

In response to your second question, I take it that you would like to see a comparison between the approximate linear simple interest growth equation given in the problem and the exact exponential compound interest growth equation used by most financial institutions such as banks.  

 

The compound interest equation (with the same input parameters given in the problem) is:

    y = 1124(1.07)^x

 

In this equation, rather than using a fixed interest amount based upon the principal, there is a compounded (added) interest amount added each year based upon all the prior years' accrued interest to the principal and expressed by the amount (1.07)^x.

 

For a visual aid in seeing the difference between the approximate linear simple interest accrual (blue graph) and the more exact compound exponential interest accrual (red graph) - click the link below to see the comparison of the two graphs:

 

https://dl.dropbox.com/s/yhxoy8lmxzp05mj/Simple_vs_Compound.png?raw=1

 

As can be seen there is no separation between the two graphs for the 1st year and still only a slight perceptible difference even after 5 years.  So we can see that the basic calculation using the simple interest formula is a good approximation for the more complex calculation involving the compound interest formula.

 

Regards, Jordan.