STEP - BY - STEP EXPLANATION
What to do?
Graph each equation on the same set of axis.
Determine the mass that makes the spring the same length.
Determine the length of that mass.
Write a sentence comparing the two springs.
Given:
f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m
Step 1
Find the x and y-intercept of both function.
f(m) = 18 + 0.4m
f(0) = 18+0.4(0) = 18
0 = 18 + 0.4m
0.4m = -18
m=-45
The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.
g(m) = 11.2 + 0.54m
g(0) = 11.2 + 0.54(0)
g(0) = 11.2
0 = 11.2+ 0.54m
0.54m = -11.2
m=20.7
The x and y - intercepts are (0, 11.2) and (20.7, 0).
Step 2
Graph the function.
Below is the graph of the function.
Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.
The length at that point is 37.4 centimeters.
Comparison between the two strings.
The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
ANSWER
b) 48.6 grams
c) 37.4 centimeters
d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).