Question

Two companies offer salaries to employees. At Company A, the salary, s, in dollars, changes at a constant rate over t years,
and can be represented by the table.



Number of Years
(
t
)

Salary
(
s
)

2

$
5800

4

$
6600

6

$
7400



The salary,
s
, in dollars, at Company B is represented by the equation
s
=
5000
(
1.07
)
t
, where
t
represents the number of years since the increase began.



Which THREE statements are TRUE about the salaries at both companies?



A.
The salaries at Company A will always differ from that of Company B.

B.
The salary at Company A is always higher than the salary at Company B.

C.
The difference between the salary at Company A and Company B after one year is less than
$
80
.

D.
The graphs representing the salaries for Company A and Company B have the same
y
-intercepts.

E.
The salary at Company B is higher for
0
<
t
≤
4
, but eventually the salary at Company A will exceed that of Company B.

F.
The salary at Company A is higher for
0
<
t
≤
4
, but eventually the salary at Company B will exceed that of Company A.

Answer 1

Answer: C, D, F.

Work:
- From the table Company A is linear. Using (2,5800): s = 400t + 5000.
- Company B: s = 5000(1.07)^t.

D: At t = 0 both give s = 5000, so they have the same y-intercept — true.

C: At t = 1, s_A = 400(1)+5000 = 5400 and s_B = 5000(1.07) = 5350; the difference is $50 < $80 — true.

F: For 0 < t ≤ 4, check examples (t = 1,2,4) and s_A > s_B in that interval. But the exponential eventually outgrows the linear; by t = 5, s_A = 7000 while s_B ≈ 7012.75, so B exceeds A for larger t — true.

A and B are false (they are equal at t = 0, and B overtakes A later), and E is false (it reverses which company is higher for 0 < t ≤ 4).