Question

Katherine has run into some good fortune. She recently received a $1000 bonus at work and decided to put it into a savings account. Her choices are a linear account that adds $30 each year or an exponential account that has 3% interest each year.
Account A - Linear
f (x) = 30x + 1000
Year
x Value
f (x)
1 $1030
2 $1060
3 $1090
4 $1120
Account B - Exponential
g (x) = 1000(1.03)x
Year
x Value
g (x)
1 $1030.00
2 $1060.90
3 $1092.72
4 $1125.51

Notice that after the first year, both accounts have the same value. Because both functions exist at the same coordinate, (1,

Answer 1

fter the first year, both accounts have the same value. Because both functions exist at the same coordinate, (1, 1030), that means f(x) = g(x) at that point. It is a solution to the system of equations.

Katherine wants to earn the most interest, so she will choose the exponential account. Exponential growth functions always exceed linear growth functions over time.

However, a third savings account has opened up. Account C is a quadratic function, h(x) = 7.84x2 + 1022.16.

How would this account compare to the other two accounts?

Is it better than the linear account?
Is it better than the exponential account?

Answer 2

To answer the question, make a table
x h(x)
-----------
0 h(0)
1 h(1)
2 h(2)
etc

h(0) (for example) is short-hand for "replace x with 0 in the formula
h(x) = 7.84x^2 + 1022.16
in other words, h(0) = 7.84* (0)^2 + 1022.16
now simplify that : 7.84*0*0 + 1022.16 = 0 + 1022.16= 1022.16

so at x=0, h(0)= 1022.16
now do the same for x=1, 2, 3,
fill in the table, and compare the numbers to the other tables they gave you.