Question

question 3 of 40
a student was given two data sets, set a and set b. which of the following statements is true?
set a

x	1	2	3	4	5
y	10	100	1000	10000	100000

set b

x	1	2	3	4	5
y	1000	1050	1100	1150	1200

a. set a is a linear function and the values increase at the same rate as set b.
b. set b is an exponential function and the values increase at a slower rate than set a.
c. set b is a linear function and the values increase at the same rate as set a.
d. set a is an exponential function and the values increase at a faster rate than set b.

Explanation:

Step1: Analyze Set A

For Set A, when $x = 1,y = 10$; when $x=2,y = 100=10^{2}$; when $x = 3,y=1000 = 10^{3}$; when $x=4,y = 10000=10^{4}$; when $x = 5,y=100000=10^{5}$. The function for Set A is $y = 10^{x}$, which is an exponential - function.

Step2: Analyze Set B

For Set B, when $x = 1,y = 1000$; when $x=2,y = 1050$; when $x = 3,y=1100$; when $x=4,y = 1150$; when $x = 5,y=1200$. The common difference $d=y_{n + 1}-y_{n}=1050 - 1000=1100 - 1050=1150 - 1100=1200 - 1150 = 50$. The function for Set B is $y=1000+(x - 1)\times50=50x + 950$, which is a linear - function.

Step3: Compare the growth rates

The exponential function in Set A grows much faster than the linear function in Set B as $x$ increases.

Answer:

D. Set A is an exponential function and the values increase at a faster rate than Set B.