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Mathematics : asked on imeldaa5009
 09.02.2023

Analyzing a function the population of bobcats in northern arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253. what does t represent? what is the domain for this function? which range values would not make sense for this function? would the graph be continuous or discrete, and why?

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17.02.2022, solved by verified expert
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Rajat Thapa
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Mathematics, DAV Post Graduate College
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"b" represents the population of bobcats.

1) "t" represents the number of years after 2008.

2) The domain (t) starts at 0 (which is the year 2008) ⇒  t ≥ 0

3) The range (b) starts when t = 0. b =-0.32(0)² + 2.7(0) + 253 ⇒ b ≥ 253

4) The graph is discrete because the population must be in whole numbers.

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Mathematics
The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253. What does t represent? What is the domain for this function? Which range values would not make sense for this function? Would the graph be continuous or discrete, and why?
Step-by-step answer
P Answered by PhD

See below.

Step-by-step explanation:

t represents time (probably years).

The population of bobcats can't be negative, so negative values in the range do not make sense.

The function is continuous, but you're probably only looking at discrete values.

Mathematics
The population of bobcats in northern arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253. what does t represent? what is the domain for this function? would the graph be continuous or discrete, and why?
Step-by-step answer
P Answered by PhD
A) t represents time ( in years ) since 2008( 2008 is zero-year)
B) Domain for the square function is x∈R, but for this kind of function there are only positive values. Firs we will find interceptions with x-axis :
t_{12} = \frac{-b\pm \sqrt{ b^{2}-4ac } }{2a}
t_{12} = \frac{-2.7\pm \sqrt{ 2.7^{2}-4*(-0.32)*253 } }{-0.64}
(calculate), t1=-24.22,  t2=32.65
Domain for this function is:  0 ≤ t ≤32.65 
C) The graph is discrete, because it is only in the first quadrant ( doesn`t have negative values ( i.e. you can`t have -10 bobcats in northern Arizona.
Mathematics
The population of bobcats in northern arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253. what does t represent? what is the domain for this function? which range values would not make sense for this function? would the graph be continuous or discrete, and why?
Step-by-step answer
P Answered by PhD
1.the number of years since 2008 
2.t values greater than or equal to 0
3.negative values 
4.discrete,because number of bobcats cannot be broken to fractional parts
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An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?
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For 1 flavor there are 9 topping

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No of choices= 5*9

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Distance=Speed*time

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