A bank uses an automated function in which a customer’s accounts will lock if they owe more than $100. Consider an equation where x is the balance of a customer’s account. What is the domain of this function?(1 point)
Responses
[0,100]
left bracket 0 comma 100 right bracket
[−100,∞]
left bracket negative 100 comma infinity right bracket
[100,∞]
left bracket 100 comma infinity right bracket
Use the image to answer the question.
Estimate the average rate of change from when x=4
to when x=5.89
.
(1 point)
Responses
approximately 6
approximately 6
approximately −0.17
approximately negative 0 point 1 7
approximately 0.17
approximately 6
The speed of an elevator (in feet per second) is modeled by the function f(x)=1.6875x
, where x is time in seconds. Estimate the average rate of change between 3.9 seconds and 8.2 seconds. Round the final answer to two decimal places.(1 point)
Responses
about 6.75 feet/second
about 6.75 feet/second
about 0.59 feet/second
about 0.59 feet/second
about 1.69 feet/second
To find the average rate of change, we need to calculate the slope of the secant line between the points where x = 3.9 seconds and x = 8.2 seconds.
The average rate of change is given by:
Average rate of change = (f(8.2) - f(3.9)) / (8.2 - 3.9)
Plugging in the values:
Average rate of change = (1.6875(8.2) - 1.6875(3.9)) / (8.2 - 3.9)
Average rate of change = (13.885 - 6.56875) / 4.3
Average rate of change ≈ 6.75 feet/second
Therefore, the average rate of change between 3.9 seconds and 8.2 seconds is about 6.75 feet/second.
f the function f(x)=6x+2
models the number of leaves on a plant x weeks after being planted, which of the following accurately calculates the average rate of change in leaves between weeks 6 and 10?(1 point)
Responses
f(b)+f(a)b−a=62+3810−6=25 leaves
f(b)+f(a)b−a=62+3810−6=25 leaves
f(b)−f(a)b−a=62−3810−6=6 leaves
f(b)−f(a)b−a=62−3810−6=6 leaves
f(b)−f(a)b+a=62−3810+6=1.5 leaves
To calculate the average rate of change in leaves between weeks 6 and 10, we use the formula:
Average rate of change = (f(10) - f(6)) / (10 - 6)
Given: f(x) = 6x + 2
Substitute the values:
Average rate of change = ((6*10 + 2) - (6*6 + 2)) / (10 - 6)
Average rate of change = (62 - 38) / 4
Average rate of change = 24 / 4
Average rate of change = 6
Therefore, the average rate of change in leaves between weeks 6 and 10 is 6 leaves.
So, the correct answer is:
f(b) - f(a) / b - a = 62 - 38 / 10 - 6 = 6 leaves