MAT-170 Exam 2 Review Name 1. The population of Northfield, New Jersey is expect

Question

MAT-170 Exam 2 Review Name 1. The population of Northfield, New Jersey is expected to increase by 1.8% every three years. The population of Northfield in 2012 was 8,624 people. Let n be the number of years since 2009. a. What is the 3-unit growth/decay factor? b. What is the 1-unit percent change? c. What is the unit growth/decay factor? d. Approximate the population of Northfield in 2009 e. Write a function P that models the population of Northfield as a function of the number of years since 2009 . Determine the number of years it will take for the population of Northfield to reach 9,172 people. 2. Let f(r) 3x 2) (3+902x -14) a. What is the degree and the leading term of this function? b. What do the degree and the leading term tell you about the end bchavior of the function? c. What are the roots of the function f? d. Compute lim f(x) and lim(x) e. Explain what happens to the behavior of the function if we change the 3x to-3x f. What happens to the behavior of the function if we remove the power 2 on the factor (x-2)2 g. What happens to the behavior of the function if we make BOTH of these changes, ie., if we change the 3x to-3x, and we remove the power 2 on the factor (x 2)2 3. Kelsie set p pennies next to a checkerboard. She then placed triple that number of pennies on the first square. Then she placed on the next square triple the number of pennies that were on the first square. She continued this pattern of always placing on the next square triple the number of pennies on the previous square. How many pennies will be on the 5th square?

Explanation / Answer

multiple questions posted.please post each question seperately

1)

a)

3-unit growth factor = (1+(1.8/100))

3-unit growth factor = (1+0.018)

3-unit growth factor = 1.018

b)

1-unit percentage change = ((1+(1.8/100))1/3 -1)*100

1-unit percentage change = ((1.018)1/3 -1)*100 exactly

1-unit percentage change = (1.005964355736237125037037085759 -1)*100

1-unit percentage change =0.5964 approximately

c)

(1/2)-unit growth factor = ((1+(1.8/100))1/3)1/2

(1/2)-unit growth factor = 1.0181/6 exactly

(1/2)-unit growth factor = 1.0029777 approximately

d)

population in 2009 = 8624*(1.018)-1

population in 2009 = 8624/1.018

population in 2009 = 8471.5127701375245579567779960707

population in 2009 = 8472 approximately

e)

P(n)=(8624/1.018)*(1.018)(n/3)

P(n)=8624*(1.018)(n/3)-1

f)

P(n)=9172

=>8624*(1.018)(n/3)-1=9172

=>(1.018)(n/3)=(9172*1.018/8624)

=>n/3=ln(9172*1.018/8624)/ln(1.018)

=>n=3*ln(9172*1.018/8624)/ln(1.018)

=>n=13.3598599

it takes 13 years for the population to reach 9172

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2)

a)

degree is 5, leading term is 18x5, leading coefficient is 18

b)

degree is odd , leading coefficient is positive, so the curve is downwards to the left ,upwards to the right.

c)

roots of function f are x=0,2,-3,7

d)

lim[x->] f(x) = ,lim[x->-] f(x) =-

e)

when 3x is changed to -3x

curve becomes upwards to the left ,downwards to the right.

f)

if we remove the power 2 on the factor (x-2)2

curve becomes upwards to the left ,upwards to the right.

g)

with both the changes

curve becomes downwards to the left ,downwards to the right.

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