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dimaraw [331]
3 years ago
14

Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding tw

o miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of
Mathematics
2 answers:
Over [174]3 years ago
7 0

Answer with explanation:

→Total Distance Ran by Sean in his first run

                      \rightarrow \frac{1}{2}=0.5

→Number of workout in miles that is run increased in a month by Sean =2 Miles

→Equation Wrote by Sean is

  f(x)= 0.5 + 2 x

This is a Linear equation in  Slope Intercept form

y = m x +c

c=0.5

m=2,which is angle made by line with positive direction of X axis.

→y=Total Distance run after x months.

→x=Number of  months=1,2,3,4,5........12,...

Slav-nsk [51]3 years ago
4 0
Variable x represents the number of runs Sean takes.
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A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,
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Answer:

  •   <u> 7,692 moose.</u>

Explanation:

The table that shows the pattern for this question is:

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A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

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  Using the first term of the sequence (0, 40) you get:

   P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

<u>  2) r</u>

Take two consecutive terms of the sequence:

  • P(0) = 40 r⁰ = 40
  • P(1) = 40 r¹ = 40r = 62
  • P(1) / P(0) = 40r / 40 = 62/40
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You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

<u>3) Model</u>

 

Thus, your model is P(x) = 40(1.55)ˣ

<u> 4) Population of moose after 12 years</u>

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The first option reduces to 1 and the second one reduces to -1.
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