A long distance phone service charges $0.30 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. U
se the greatest integer function to write the cost C of a call in terms of time t (in minutes). Sketch the graph of this function and discuss its continuity.
1 answer:
Answer: Our Cost function is discontinuous at every integer after x>10.
Step-by-step explanation:
Since we have given that
For the first 10 minutes , the service charges = $0.30
Let the number of additional minute be 't'.
Amount charge for each additional minute = $0.05
Using the greatest integer function:
So, Cost C of a call in terms of time 't' minutes would be
As we know that Greatest integer is discontinuous at every integer.
So, our Cost function is discontinuous at every integer after x>10.
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Answer:
A. Both of Johny's (f(x)) and David's functions (g(x)) are linear.
B. (f(x) - 75) ∝ x and g(x) ∝ x
where x = no. of working hours,
f(x), g(x) = money saved
C. Equation for Johny is,
y = 75 + 10x
where, x = no. of hours Johny works
y = money saved by Johny.
D. Equation for David is,
y = 20x
where, x = no. of hours David works
y = money saved by David
E. David will buy the X-box earlier. it can be found by putting f(x) = g(x) = 200 in the two equations and from that comparing the two values of x.
Step-by-step explanation:
Let the equation for Johny be,
y = mx + c
where c is the y intercept which is here 75 and m is the slope of the straight line which is here ,
m =
= 10 [since (125 ,5) and (75 ,0) are over the straight line]
So, Johny's equation is,
y = 10x + 75 = f(x) [say]-------------------------------------------------(1)
which is linear.
Now slopes of different straight lines connecting the points for David are all equal to 20 ,
[since,
=
=
=
=
= 20]
So, David's equation is also a straight line with y intercept 0 and slope 20.
So, David's equation is,
y = 20x = g(x) [say] --------------------------(2)
A. Now, from (1) and (2) both of Johny's and David's functions are linear.
B. From (1) (f(x) - 75) ∝ x and from (2) g(x) ∝ x
C. Equation for Johny is,
y = 75 + 10x
where, x = no. of hours Johny works
y = money saved by Johny.
D. Equation for David is,
y = 20x
where, x = no. of hours David works
y = money saved by David
E. Putting y = 200 in (1) we get,
125 = 10x
⇒12.5 , so, Johny will earn the money in 12.5 hours.
and, putting y = 200 in (2) we get, x = 10 so, David will earn the money in 10 hours. since, 10 < 12.5 so, David will be able to purchase the X-box first.