A local bakery opened with new equipment worth $80,000. Ten years later, the owners’ accountants told them that their equipment had depreciated at a rate of 6 percent per year. Which equation would you use to create a sequence modeling this situation?(1 point)

Question

A local bakery opened with new equipment worth $80,000. Ten years later, the owners’ accountants told them that their equipment had depreciated at a rate of 6 percent per year. Which equation would you use to create a sequence modeling this situation?(1 point)
Responses

an=80,000(0.06)n
a subscript n baseline equals 80,000 left parenthesis 0.06 right parenthesis superscript n baseline

an=80,000(0.94)n
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n baseline

an=80,000(0.94)n−1
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n minus 1 baseline

an=80,000(0.06)n-1

In a certain geographic location, a herd of elephants is declining at a rate of four percent every year. If there are currently 62 elephants in the herd, create an exponential decay function to model the problem. Let y represent the number of elephants after t years.(1 point)
Responses

y=62(0.6)t
y equals 62 left parenthesis 0.6 right parenthesis superscript t baseline

y=62(1.04)t
y equals 62 left parenthesis 1.04 right parenthesis superscript t baseline

y=62(0.96)t
y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline

y=62(0.04)t

Use the table to answer the question.

Years (t)	0	5	10	15	20
Number of Birds (y)	 	 	 	 	 
Complete the input-output table and determine which graph matches the sequence of the decay rate of a specific species of bird modeled by the equation  y=4,060(0.95)t .

(1 point)
Responses

A. A coordinate plane's x-axis ranges from 0 to 30 by 5-unit increments and its y-axis ranges from 0 to 6000 by 1000-unit increments. The x-axis is labeled 'Years' and the y-axis is labeled 'Number of Birds.'
Image with alt text: A coordinate plane's x-axis ranges from 0 to 30 by 5-unit increments and its y-axis ranges from 0 to 6000 by 1000-unit increments. The x-axis is labeled 'Years' and the y-axis is labeled 'Number of Birds.'

B. A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 0 to 600 in increments of 20. There is an arrow at the decreasing end.
Image with alt text: A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 0 to 600 in increments of 20. There is an arrow at the decreasing end.

C. A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 10 and 'Number of Birds' on the y-axis ranging from 0 to 6000. There is an arrow at the decreasing end.
Image with alt text: A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 10 and 'Number of Birds' on the y-axis ranging from 0 to 6000. There is an arrow at the decreasing end.

D. A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 40,000 to 52,000 in increments of 400. There is an arrow at the decreasing end.
Image with alt text: A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 40,000 to 52,000 in increments of 400. There is an arrow at the decreasing end.
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Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 10 to 10, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a marked point on the y-axis.

Use the graph of the exponential decay function that models an exponential decay sequence to discuss the properties and determine the equation for the horizontal asymptote of the graph.

(1 point)
Responses

The horizontal asymptote is at y=0.
The horizontal asymptote is at y equals 0 .

The horizontal asymptote is at y=−7.
The horizontal asymptote is at y equals negative 7 .

The horizontal asymptote is at y=5.
The horizontal asymptote is at y equals 5 .

The horizontal asymptote is at y=0.3.

Which graph has the following properties?

The y-intercept is at  (0,22) .
The horizontal asymptote is at  y=5 .
The graph is decreasing for all values of x.
(1 point)
Responses

A. A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. 
Image with alt text: A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.

B. A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. 
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.

C.  A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis. 
Image with alt text: A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis.

D A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.

GPT-4o mini · Answer

Let's analyze the questions one by one.

Local Bakery Equipment Depreciation:

The equipment is worth $80,000 and depreciates at a rate of 6% per year. To find the value of the equipment after $ n $ years, we multiply the initial value by $ (1 - \text{depreciation rate})^n $. In this case, the depreciation rate is 6%, so the remaining value each year is 94% of the previous value. Thus, the equation will be:

\[ a_n = 80,000(0.94)^n \]

So, the correct response is:

an=80,000(0.94)n

Declining Herd of Elephants:

The herd declines at a rate of 4% per year from an initial count of 62 elephants. The function for exponential decay can be modeled as:

\[ y = 62(1 - 0.04)^t \] \[ y = 62(0.96)^t \]

Therefore, the correct response is:

y=62(0.96)t

Birds Modeling with Function:

Using the equation $ y = 4,060(0.95)^t $, we can calculate the number of birds after the specified years:

For $ t = 0 $: $ y = 4,060(0.95)^0 = 4,060 $
For $ t = 5 $: $ y = 4,060(0.95)^5 \approx 3,197 $
For $ t = 10 $: $ y = 4,060(0.95)^{10} \approx 2,268 $
For $ t = 15 $: $ y = 4,060(0.95)^{15} \approx 1,674 $
For $ t = 20 $: $ y = 4,060(0.95)^{20} \approx 1,200 $

Now, we match these numbers with the graphs. Given the description and increments provided, the graph should show a consistent decrease and fit these calculated values.

Answer: Without the graphs provided, I'm unable to specify exactly which option fits best. Please look for decreasing trends matching the calculated points.

Horizontal Asymptote:

For exponential decay functions, the horizontal asymptote generally approaches the x-axis (y=0) as time (t) goes to infinity. Therefore, the horizontal asymptote for the exponential decay functions is at:

The horizontal asymptote is at y=0.

Graph with Specific Properties:

The graph properties state that it has a y-intercept at (0,22), a horizontal asymptote at y=5, and is decreasing for all values of x. To find the correct graph:

The specific y-intercept of (0,22) indicates a starting point above the horizontal asymptote. Thus, we are looking for a decreasing function starting above y=5.

Based on your description, the graph must be consistent with these properties. Look for a graph option indicating a point at (0,22) and an asymptote at y=5:

The answer would be: Check the descriptions in the images provided for those exact properties.

Please review and match these insights with your provided graphics and descriptions for the best responses!