CM 5.3 Exponential Functions: Growth and Decay

Which of the following functions represents exponential growth?

Which of the following scenarios best describes exponential decay?

• A tree growing taller each year

• A balloon deflating over time

• A bank account earning interest

• A population of rabbits increasing

Answer explanation

Exponential decay refers to a process where a quantity decreases at a rate proportional to its current value. A balloon deflating over time exemplifies this, as the volume decreases rapidly at first and slows down as it empties.

Tags

CCSS.HSF-LE.A.1A

Which of the following equations represents exponential decay?

Which of the following best describes a situation of exponential growth?

• A car losing value over time

• A bank account with compound interest

• A melting ice cube

• A candle burning down

Answer explanation

A bank account with compound interest exemplifies exponential growth, as the interest earned increases over time, leading to a rapid increase in the account balance. This contrasts with the other options, which do not exhibit exponential growth.

Which of the following functions represents a situation where the quantity is halved every time period?

Answer explanation

The function f(x) = 100 \cdot 0.5^x represents a situation where the quantity is halved every time period, as 0.5 indicates a reduction to half of the previous amount with each increase in x.

Tags

CCSS.HSF.LE.A.2

What is the growth factor?​ (a)  

Assuming the trend continues, how many houses will there be in Month 4?​ (b)  

How many houses in Month 5? (c)  

How many houses in Month 6? ​ (d)  

• 36

• 48

• 96

• 60

• 72

• 24

• 2

Answer explanation

The growth factor can be determined by the pattern of house increase. If Month 1 has 24 houses, Month 2 has 48 (double), Month 3 has 96 (double again). Thus, Month 4 will have 48 houses, Month 5 will have 96, and Month 6 will have 24.

Tags

CCSS.HSF.BF.A.2

Which of the following functions represents a situation where the quantity doubles every time period?

Answer explanation

The function f(x) = 50 \cdot 2^x represents exponential growth where the quantity doubles every time period. The base 2 indicates that for each increase in x, the output is multiplied by 2.

Tags

CCSS.HSF.LE.B.5

Which of the following scenarios best describes exponential growth?

• A population of bacteria doubling every hour

• A car depreciating in value

• A piece of metal cooling down

• A candle burning at a constant rate

Answer explanation

Exponential growth occurs when a quantity increases by a consistent percentage over time. A population of bacteria doubling every hour exemplifies this, as it grows rapidly and continuously, unlike the other scenarios which depict linear or diminishing changes.

Tags

CCSS.HSF-LE.A.1A

Which of the following equations represents a situation where the quantity decreases by 25% each time period?

Answer explanation

The equation y = 200 \cdot 0.75^x represents a quantity that decreases by 25% each time period, as 0.75 is equivalent to 1 - 0.25. The other options either increase or decrease by different rates.

Tags

CCSS.HSF.LE.A.2

Which of the following functions represents a situation where the quantity triples every time period?

Answer explanation

The function f(x) = 30 · 3^x represents exponential growth where the quantity triples (multiplies by 3) for each unit increase in x. The other options either grow slower or decay.

Tags

CCSS.HSF.LE.A.2