# DETERMINE IF THE GIVEN FUNCTIONS ARE EXPONENTIAL EQUATIONS

Linear function :

If the growth or decay involves increasing or decreasing by a fixed number(constant difference), then it should be a linear function.

y = mx + b

b is y-intercept and m is slope.

Exponential function :

If the growth or decay involves using multiplication, then it should be a exponential function.

y = a(b)x

a is starting value

If b > 0 for growth and 0 < b < 1 when it is decay.

Decide whether the word problem represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula.

Problem 1 :

“A library has 8000 books, and is adding 500 more books each year.” Linear or exponential?

y = __________________.

Solution :

Number of books initially has = 8000

Let x be the number of years they are adding.

y = 8000 + 500x

It is linear function.

Problem 2 :

“A gym’s customers must pay \$50 for a membership, plus \$3 for each time they use the gym.” Linear or exponential?

y = __________________.

Solution :

Let x be the number of times he is going for gym.

Membership fee = \$50

y = 50 + 3x

So, it is linear function.

Problem 3 :

“A bank account starts with \$10. Every month, the amount of money in the account is tripled.” Linear or exponential?

y = __________________.

Solution :

Writing down the deposits of each month

10, 30, 90, .............

Multiplication factor (b) is 30/10 ==> 3

a = 10 and b = 3

Let x be the number of  months.

y = a(b)x

y = 10(3)x

Problem 4 :

“At the start of a carnival, you have 50 ride tickets. Each time you ride the roller coaster, you have to pay 6 tickets.” Linear or exponential?

y = __________________

Solution :

Number of tickets that i am having = 50

Every time i ride, will loss 6 tickets.

Let x be the number of times i am riding.

y = 50 - 6x

So, it is linear function.

Problem 5 :

“There are 20,000 owls in the wild. Every decade, the number of owls is halved.” Linear or exponential?

y = _____________

Solution :

20000, 10000, 5000, ..........

Multiplication factor = 10000/20000

= 1/2

a = 20000 and b = 1/2

Let x be the number of years.

y = 20000(1/2)x

So, it is exponential function.

Problem 6 :

A science experiment involves periodically measuring the number of mold cells present on a piece of bread. At the start of the experiment, there are 50 mold cells. Each time a periodic observation is made, the number of mold cells triples.

a) Write a function formula equation (y = ···) for the number of mold cells present, where x stands for the observation number.

b)

Solution :

Number of molds cells initially = 50

Each time the number of mold cells triples.

Multiplication factor = 3

From this information, it is clear, it should be exponential function..

a = 50 and b = 3

y = 50 (3)x

 Observation number(x)012345 Mold cell count(y)501504501350405012150

Problem 7 :

Ms. Hunter takes off 10 points for each day an assignment is turned in late. The assignments are worth 100 points each.

Solution :

Every day decreases 10 points.

Worth of the assignment = 100

Let x be the number of times taking off.

y = 100 - 10x

So, it is a linear function.

Problem 8 :

There are 200 ladybugs in a certain population. The population is decreasing by 14% per day.

Solution :

Number of lady bug = 200

Decreasing = 14% per year.

Let 100% of ladybugs are there initially.

Every year 86% of original number of lady bugs will be there in the next year.

Let x be the number of years.

After x number of years, number of lady bugs

= 200 (86/100)x

It is exponential function.

Problem 9 :

Your salary starts at \$23000 and goes up by 5% per year.

Solution :

Starting salary = 23000

Every year goes up 5%.

If initial salary be 100%, then 105% of the proceeding year salary will be the salary of next year.

y = 23000(105/100)x

Problem 10 :

A painter is going to charge \$90 for paint and \$35 an hour to paint your kitchen.

Solution :

Let x be the number of hours that painter paints in your kitchen.

y = 90 + 35x

So, it is linear function.

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