6G Linear and Exponential Review

When given a list of numbers, you must find the “zero” <y-intercept> number in the sequence by subtracting or multiplying by the reciprocal. Then write the equation.

Linear: y = mx + bExponential: y = a(b)x

Ex: 6, 10, 14 …..  The ‘Zero’ number of the sequence is 6 -2 = 4. Equation: y = 4x + 2

Ex: 3, 6, 12  The ‘Zero’ number of the sequence is 3*1/2 = 1.5 Equation: y = 1.5(2)x

Find the equation of the following:

  1. 5, 7, 9 …2. 2, -2, -6 ..3. 5, 10, 20… 4. 8, 2, .5…
  1. On the first day, there are 8 flowers. On the second day, there are 11 flowers. On the third day, there are 14 flowers.
  1. Write the equation that describes the situation where ‘d’ is the number of days since the beginning of the month.
  2. Find how many flowers there are on the 12th day.
  3. Find when there will be 71 flowers.
  1. In the first month, there are 6 rabbits. In the second month, there are 12 rabbits. In the third month, there are 24 rabbits.
  1. Write the equation that describes the situation where ‘m’ is the number of months.
  2. Find how many rabbits there are on the 6th month?
  3. In what month will there be more than 300 rabbits?
  1. On the second day, Jane receives 20 text messages. On the 4th day, she receives 28 text messages. On the 7th day, she receives 40 text messages.
  1. Write an equation.
  2. How many text messages does she receive on the 12th day?
  3. On what day does she receive at least 100 text messages?
  1. *Jane has $5000 in her savings account. Each month, she puts in $500.

*Ted has $5000 in his savings account. Each month, he puts in 5% more.

  1. Write an equation that models each situation

Jane:Ted:

  1. Approximately when will they have the same amount in their savings account?
  1. Jason makes 100$ a month plus 5% commission on what he sells.
  1. Write an equation that models his income
  1. How much does he have to sell to make $2000 this month?
  1. Jack makes $1000 the first month. His salary increases by 3% every month.
  1. Write an equation that models his income
  2. How much will he make 10 months later?
  3. At what month will he triple his income?

11-13.Write equations for the following tables:

X / 1 / 3 / 6 / 8
Y / 7 / 13 / 22 / 28

y =

X / 1 / 2 / 4
Y / 8 / 16/5 / 64/125

y=

X / 3 / 6 / 11 / 14
Y / 5 / 11 / 21 / 27

y=

12.Fill in the table based on the following information:

Ashley and Olivia each had $5 in their savings accountwhen they began their new jobs.

  • For Ashley, at the end of each week $20 was added to her account.
  • For Olivia, at the end of each week her account balance was doubled.
  1. How much was in Ashley’s account at the start of week 3?
  2. How much was in Olivia’s account at the start of week 5?
  3. At the start of which week will Olivia have more money than Ashley?
  4. Write an equation to model each person’s bank account:

BAshley = BOlivia =

13. Nathan and Woody have Twitter accounts, and both have 500 followers.

At the end of each week, the number of Nathan’s followers triplesand .

the number of Woody’s followers increases by 4000.

  1. How many followers did Woody have at the start of week 2?
  2. How many followers did Nathan have at the start of week 2?
  3. At the start of which week will Nathan have more followers than Woody?
  4. Write an equation to model each person’s number of followers:
  5. FNathan = FWoody =

14.Jaquan and Rita are playing a game. Both Jaquan and Rita have 150 points.

  • At the end of each turn, Jaquan’s points are doubled.
  • At the end of each turn, Rita’s points are increased by 600.
  1. At the start of which turn will Jaquan have more points than Rita?
  2. Write an equation to model each person’s number of points:

PJaquan = PRita =

15. Amy and Marie collect stamps.- Both Amy and Marie have 20 stamps.

  • At the end of each week, the number of stamps Amy has is increased by 80.
  • At the end of each week, the number of stamps Marie has is doubled.

a. At the start of which week will Marie have more stamps than Amy?

b. Write an equation to model each person’s number of stamps:

NAmy = NMarie =

16.Max and Greg are playing a game. Both Max and Greg have 400 points.

  • At the end of each turn, Max’s points are increased by 2000.
  • At the end of each turn, Greg’s points are doubled.

a. At the start of which turn will Greg have more points than Max?

b. Write an equation to model each person’s number of points:PMax = PGreg =

17. Bonnie and Jayne collect pairs of earrings. Both Bonnie and Jayne have 8 pairs.

  • At the end of each month, the pairs of earrings Bonnie has is increased by 30.
  • At the end of each month, the pairs of earrings Jayne has is doubled.
  1. At the start of which month will Jayne have more pairs of earrings than Bonnie?
  2. Write an equation to model each person’s number of pairs of earrings:NBonnie = NJayne =

18. Jimmy and Ray are playing a game. Both Jimmy and Ray have 300 points.

  • At the end of each turn, Jimmy’s points are 1.5 times the points before.
  • At the end of each turn, Ray’s points are increased by 1000.

a. At the start of which turn will Jimmy have more points than Ray?

b. Write an equation to model each person’s number of points:PJimmy= PRay =

19. The population of Rabbitville increased exponentially since 1980. In 1980, the population was 2 million. In 1981, the population was 2.5 million.

  1. Write an equation that models this function?
  2. How many rabbits were there in 1990?

20. *A: The number of bacteria divides into three every 15 minutes. There were 3 bacteria at 1:00 PM.

*B: The number of bacteria divides into seven every 4 hours. There were 3 bacteria at 1:00 PM

  1. Write an equation that models each behavior. Let t represent the number of hours.

A: B:

  1. Find the number of bacteria at 1:00 AM for each. A:B:

21. Situation A: 2x – y = 8 Situation B: Daisy makes 5$ and hour plus 10% of her tips.

  1. Find the difference of the y-intercepts between situation A and situation B.
  2. Find the difference of the slopes between situation A and situation B.

22.Situation A: Next = Now * 4 starting at 7 Situation B: y = 3x

Find the difference of the y-intercepts between Situation A and Situation B

23. Determine if the following are exponential (E) or linear (L) equations. Then write the equation.

  1. A taxi charges a flat-fee of $5 and charges $3 per mile ______
  2. The value of a $200,000 house increases by 5% daily ______
  3. There are 200 gallons in a lake. It loses 23% a month. ______
  4. There are 20 gallons in a bath tub. It loses 3 gallons every minute ______
  5. Water is removed from a stove at 212o F. It loses 20% of its temperature every minute______
  6. The temperature at Noon is 75oF. It gains 2 degrees every minute______
  7. Sally is on a diet and starts with 200 pounds. She loses 4 pounds a week.______
  8. A baby is gaining weight by 2.5% a month. It started at 16 pounds. ______

24-28. Determine if each column represents exponential growth or linear growth?

24. Water amount (gallons) / 25. Soda (oz) / 26. Amount of Blood (pints) / 27. Temperature in Nome (Fo) / 28. Body temperature (Fo)
0 Hour / 15 / 10 / 7 / 30.5 / 35
1 Hour / 21 / 15 / 8.4 / 32.3 / 28
2 Hours / 26 / 22.5 / 10.1 / 34.1 / 22.4
3 Hours / 31 / 33.75 / 12.1 / 35.9 / 17.9
4 Hours / 36 / 50.6 / 14.5 / 37.7 / 14.3
5 Hours / 41 / 75.9 / 17.5 / 39.5 / 11.5
Exponential or Linear?

29.Fill in the chart.

Equation / Next-Now / First 3 Numbers / Situation
A cab charges a flat fee of 4$ and .70 per 1/10th of a mile
8, 12, 18
Next = Now*4
Starting at 7
y=2x
Next = Now + 3 starting at 4

30-39 For each question write a NEXT/NOW equation and a y= equation (linear or exponential).

x / Y
-1 / -2
0 / 1
1 / 4
x / y
0 / -9
1 / -4
2 / 1

30. 31. 32.33.

34. (0, 3) (1, 6) (2, 12) 35. (0, -3) (1, -2.5) (2, -2)

y= Next = Now S.A. y = Next = Now S.A

36. The bacteria in a Petri dish triples every hour. Initially there were 5 bacteria.

37. Sarah’s babysitting job pays $7 per hour and she gets paid $5 for gas money.

38. David had $20 at the beginning of the week. Each day he spent $3.50 on lunch.

39. Nancy bought a car for $35,000. The value of her car depreciates at 10% each year.