sgrowing linearly. In 2000, the state had 15.9 Million Find the n of Florida on

Question

sgrowing linearly. In 2000, the state had 15.9 Million Find the n of Florida on was 18.5 Million. Find the equation for the le. and in 2011 the population people, an ound decimals to the nearest thousandth. 2. Use your equation (answer) from Problem 1 above to calculate the Population of Florida in 2018. Write your answer in a complete math sentence using function notation 3. Kim's test scores in MAC1105 increase with the amount of time she studies in a linear fashion. When she studies for 2 hours, Kim gets a 60. When she studies for 4 hours, she gets an 82. Write an equation for Kim's test seore (S) as a function of the number of hours she studies, t 4. Use your equation from problem 3 to figure out how many hours Kim needs to study in order to get a 94. Since this is a word problem, decimals are ok, but I want to see linear-equation-solving work.

Explanation / Answer

1. Let P(t) is the popuation (in million) in tth year

Acc. to question P(t) = mt + c where m and c are constant

P(2000)= 15.9

P(2011)= 18.5

15.9 = 2000m +c

18.5 = 2011m +c

=> 11m = 2.6

=> m =0.2364

=> c= 15.9*2011 - 18.5*2000

=> c= -456.872

So P(t) = 0.2364t - 456.872

2.

P(2018) =0.2364t - 456.872

=0.2364*2018 - 456.872

=20.18 million

3.

S(t) = mt+c

S(2) = 60

S(4) = 82

60= 2m +c

82= 4m +c

=> 2m = 22

=>m=11

c= (120 - 82)

c= 38

Therefore S(t) = 11t + 38

4. S(t) = 11t + 38

S(t) = 94, t= ?

94 = 11t + 38

11t = 56

t= 56/11 = 5.0909 hours

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