A Saving account has a balance of $1 . Savings plan A will add $1000 to an account each month , and plan B will double the amount each month ?
a. Which plan is better in the short run ? for How long , Explain.
b. Which plan is better in the long run ? Explain.

The correct answer is: Plan A is better in the short run for around 13 months. After which, Plan B is better in the long run.

Step-by-step solution:-
From the given information, we get-
Opening balance in Savings account = $ 1.
Let the function be represented by 'y'.
For Savings plan A-
Rate of change = +1,000 every month.
Since every month the same amount is added to the balance, the first difference = constant = 1,000.
Hence, Savings plan A can be represented by a linear function.
A linear function is always represented in the form-
                                            Y = a + bX ....................................... (where a represents the starting point and b represents the common difference)
                                         ∴ Y = 1 + 1,000X ................................ (starting point is $ 1 and rate of increase is 1,000) .................. (Equation i)
For Savings plan B-
Rate of change = *2 every month.
Since ratio of balance in every consecutive month will remain the same i.e. 2 because every month balance will be doubled, Savings plan B can be represented by an exponential function.
A linear function is always represented in the form-
                                           Y = aX ....................................... (where a represents the rate of change)
                                        ∴ Y = 2X ....................................... (Rate of change is 2 times every month) .......................................... (Equation ii)
We can plot the above equations on a graph and observe the movement.
a). As we observe from the adjacent graph, in the short run, Savings plan A is better.
This trend can be observed till around the 13th month. From the 14th month, Savings in Plan B exceeds the savings from Plan A.
b). As we observe from the adjacent graph, in the long run, Savings plan B is better.
Final Answer:-
∴ Plan A is better in the short run for around 13 months. After which, Plan B is better in the long run.