Part A)
f(x) = 5^x
f(0) = 5^0
f(0) = 1
----------
f(x) = 5^x
f(1) = 5^1
f(1) = 5
----------
f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
----------
f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125
-------------------
Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4
Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100
================================================
Part B)
From part A) above, we found,
Rate of change for section A = 4
Rate of change for section B = 100
Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)
Answer for part B: 25
================================================
Extra: Explain why one rate of change is greater than the other.
The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed.
Answer:
A. y >= 0
Step-by-step explanation:
The range of a function is the set of all values that the y-coordinate can have.
Look at the graph. Look at the red curve. The lowest y-coordinate is 0. As the curve goes up to the right, the y-coordinates are all real numbers greater than or equal to 0.
Answer: A. y >= 0
Answer:
$339.25
Step-by-step explanation:
Since the credit card customer owes $523.85 and is only able to make a payment of $184.50
Amount still owed
= $523.85 - $184.60
= $339.25
The customer still owes $339.25
Slope is the change in y over the change in x.
Using the red dots:
Slope = (4 -1)/(4- -1) = 3/5
Slope = 3/5
