The table shows the height of a model rocket launched from the top of a four-story building and landing in a pond nearby. Height is measured in feet above the surface of the pond. Rocket Height Time, t (seconds) Height, H (feet) O (launch) 61 0.5 73 1. 77 1.5 73 2 61 (a) Explain why a quadratic model is more appropriate than a log or exponential model. The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. The data indicates a maximum point and changes from increasing to decreasing at that point. Logarithmic and exponential functions do not possess maximum points, but quadratic functions do. The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do. The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Write the function for the quadratic model that gives the height in feet of the rocket above the surface of the pond, where t is seconds after the rocket has launched, with data from osts 2.
The table shows the height of a model rocket launched from the top of a four-story building and landing in a pond nearby. Height is measured in feet above the surface of the pond. Rocket Height Time, t (seconds) Height, H (feet) O (launch) 61 0.5 73 1. 77 1.5 73 2 61 (a) Explain why a quadratic model is more appropriate than a log or exponential model. The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. The data indicates a maximum point and changes from increasing to decreasing at that point. Logarithmic and exponential functions do not possess maximum points, but quadratic functions do. The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do. The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Write the function for the quadratic model that gives the height in feet of the rocket above the surface of the pond, where t is seconds after the rocket has launched, with data from osts 2.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...
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Transcribed Image Text:The table shows the height of a model rocket launched from the top of a four-story building and landing in a pond nearby. Height
is measured in feet above the surface of the pond.
Rocket Height
Time, t
(seconds)
Height, H
(feet)
O (launch)
61
0.5
73
77
1.5
73
2
61
(a) Explain why a quadratic model is more appropriate than a log or exponential model.
The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease
while quadratic functions either increase or decrease.
The data indicates a maximum point and changes from increasing to decreasing at that point. Logarithmic and
exponential functions do not possess maximum points, but quadratic functions do.
The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and
exponential functions do not possess minimum points, but quadratic functions do.
The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease
while quadratic functions either increase or decrease.
(b) Write the function for the quadratic model that gives the height in feet of the rocket above the surface of the pond,
where t is seconds after the rocket has launched, with data from osts 2.
H(t) =
(c) Use the model to determine when the missile hits the water. (Round your answer to two decimal places.)
sec
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