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2 answers:
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Answer:
A. perhaps 0 to 7 days
B. the radius in mm at the start of the study
C. 0.114 mm/day
Step-by-step explanation:
A. It is always problematic to determine the reasonable domain for an exponential growth function. You can always limit the domain to the length of time for which the function is said to model the growth. It is difficult to say how much beyond that time period the exponential growth can be extrapolated, as most systems run into limits to growth.
Here, the base of the exponential term is 1.01 = 1 + 1%. This tells you the growth rate is 1% per day. The study concludes when the radius was 11.79/11.00 = 1.071818... ≈ 1 + 7.2% times the original size. That is, the study lasted approximately 7 days.
The question in part C has you look at the size on day 7, which is apparently the last day of the study. It is not clear that the model is at all useful beyond the end of the period it is intended to describe.
A reasonable domain for the growth function is 0 to 7 days.
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B. The function gives the radius of the algae after d days. When d=0 (the y-intercept), the function gives the radius of the algae after 0 days. That is the meaning of the y-intercept is the initial radius of the algae (at the beginning of the study).
The y-intercept is always the "initial value", the value when the independent variable is zero. You have to look at the function definition to see what it is the initial value of.
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C. The average rate of change is the difference in function values divided by the difference in time between them. Here, the attached table tells us that is ...
(f(7) -f(2))/(7 -2) = (11.793 -11.221)/5 = 0.572/5 = 0.1144 . . . mm/day
The units of the "average rate of change" are the units of the slope of the curve on the graph: the y-axis units divided by the x-axis units. Here, that is mm/day.
Answer:
The bus drives 84 miles
Step-by-step explanation:
The question relates to relationship between average speed and time
The given parameters are;
The time duration in which the bus drives = 3/2 hours = 1.5 hours
The average speed of the bus = 56 mph
The formula average speed is given as follows;
Therefore, we have;
The total distance driven = Average speed × The time duration of travel
The total distance driven = The distance the bus drives
Substituting the given values, gives;
The distance the bus drives = 56 miles/hour × 1.5 hours = 84 miles
The distance the bus drives = 84 miles.