Question

Violet and Toby deposit money into their savings accounts at the end of each month. The table shows the account balances. If their patterns of saving continue, and neither earns interest nor withdraws any of the money, how will the balances compare after a very long time?

Answer 1

can you specify a very long time

Answer 2

Answer: C. Taby's balance will be greater.

Explanation:

From the given table, it can be seen that there is constant rate of change in money in account of Violet of $20 per month .

⇒ There is linear growth in Violet's month balance.

Linear function is given by :-

`y=mx+c`, where m is slope and c is the initial value.

At x=1 , y=30 and slope (m) = 20 , we have

`30=20(1)+c\\\\\Rightarrow\ c=10`

∴ Equation for Violet's balance after x months :

`y=20x+10`

For Taby, there a money is increasing with multiplicative growth or exponential growth.

Let be be the growth rate .

`b=(6)/(3)=2`

Exponential growth is given by :-

`y=Ab^x`, where A is initial value m, b is growth factor and x is time period.

At x=1, y=3 and b = 2, we have

`3=A(2)^1\\\\\Rightarrow\ A=1.5`

∴ Equation for Taby's balance after x months :

`y=1.5(2)^x`

Since the graph of a linear function is a line, whereas the graph of an exponential growth function is a curve that increases slowly at first, then more quickly.

After a very long time period the exponential function gives greater value as compare to the linear function .

∴ Taby's balance will be greater.