Answer: C. Taby's balance will be greater.
Step-by-step 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 :-
[tex]y=mx+c[/tex], where m is slope and c is the initial value.
At x=1 , y=30 and slope (m) = 20 , we have
[tex]30=20(1)+c\\\\\Rightarrow\ c=10[/tex]
∴ Equation for Violet's balance after x months :
[tex]y=20x+10[/tex]
For Taby, there a money is increasing with multiplicative growth or exponential growth.
Let be be the growth rate .
[tex]b=\dfrac{6}{3}=2[/tex]
Exponential growth is given by :-
[tex]y=Ab^x[/tex], 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
[tex]3=A(2)^1\\\\\Rightarrow\ A=1.5[/tex]
∴ Equation for Taby's balance after x months :
[tex]y=1.5(2)^x[/tex]
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.
