Exponential Compounding Word Problems

If a population of 300 animals in a certain region is growing exponential at 2% per year, when will the population reach 400?

• 14.4 years

• 15 years

• 6.2 years

• 20 years

Miguel had 25 bacteria in his petri dish at 2 PM. There were 72 in the dish at 2:30 PM. Assuming exponential growth, at what rate are they increasing?

• 9.6% per minute

• 0.03526% per minute

• 35.26% per minute

• 3.526% per minutes

The population of Guyana was roughly 787,000 in 2020 and 747,000 in 2000. If the population is growing exponentially, what is the rate of growth?

• 0.002608

• 0.00113

• 0.0527

• .2608

The population of Pallet Town increases by 15% every year. If there are currently 190,000 people living there, what will be the population in 13 years?

If necessary, round your answer to the nearest whole number.

• 4 people.

• 22,972 people.

• 1,169,030 people.

• 1,188,311 people.

Eduardo currently has 500 followers on TikTok. He makes a video after the basketball game and it goes viral! Since he became internet famous, the number of followers is increasing by 25% daily. Write an exponential function that represents the relationship between x, the number of days since Eduardo posted the video and y, the total number of followers Eduardo has.

Mathematical Equivalence

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A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

y = ​ (a)   ( 1 ​ (b)   ​ (c)   )^x (^ means to power of x - x is the exponent)

• 400

• +

• 0.03

• 3

• 0.3

• 0.97

• 4

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

• y = 30,010 (.05)^x

• y = 30,010 (1.05)^x

• y = 30,010 (.95)^x

• y = 30,010 (5)^x

Find the balance in an account that has $300 invested at 6.5% for 4 years compounded semi-annually.

• $387.47

• $496.50

• $7,800.00

• $385.94

Derrick has $1,000 in a savings account that ears 15% interest, compounded monthly. To the nearest cent, how much will he have in 2 years?

• $5,350.25

• $1,322.50

• $1,025.16

• $1,347.35

Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year.

To the nearest cent, how much will he have in his account in 4 years?

• $9,004.07

• $2,2848.80

• $9,011.94

• $8,242.71