Question

if $20000 is invested at 6% simple interest, the initial value and the future value s at the end of each of 5 years is shown in the table below. then answer part (a) through (d).

year (t)	future value ($)
1	2120
2	2240
3	2360
4	2480
5	2600

(a) can a linear function model exactly the points from the table? explain.
a. no, the first differences are not constant for uniform inputs.

b. yes, the first differences are constant for uniform inputs.

Explanation:

Step1: Calculate first differences

$2120 - 2000 = 120$
$2240 - 2120 = 120$
$2360 - 2240 = 120$
$2480 - 2360 = 120$
$2600 - 2480 = 120$

Step2: Analyze linear function condition

Uniform input intervals (1 year) and constant first differences mean the relationship is linear.

Answer:

B. Yes, the first differences are constant for uniform inputs.