Maths-

General

Easy

Question

# 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.

Hint:

### 1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.

2. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. y(n)/y(n-1) is constant for any value of n, the function is known as an exponential function.

## 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.

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