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.

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.

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.5.OA.B.3

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.

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.

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.

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.