Exponent Word Problem

A bacteria culture starts with 1000 bacteria and doubles every hour. Write an exponential expression to represent the number of bacteria after x hours.

• 1000 / 2^x

• 1000 * x^2

• 1000 * 2^x

• 1000 + 2^x

If a car depreciates by 20% each year, write an exponential expression to represent the value of the car after x years if it was originally worth $10,000.

• $10,000 * (0.8)^x

• $10,000 * (0.2)^x

• $10,000 * (1.2)^x

• $10,000 * (0.5)^x

A radioactive substance decays by 30% every 5 hours. Write an exponential expression to represent the amount of substance remaining after x hours if the initial amount was 500 grams.

• 500 * (0.7)^(x/5)

• 500 * (0.3)^(x/5)

• 500 * (0.7)^(x)

• 500 * (0.3)^(5/x)

A population of rabbits triples every month. Write an exponential expression to represent the population after x months if there were originally 50 rabbits.

• 50 * x^3

• 50 * 3x

• 50 * 3^x

• 50 + 3^x

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

If an investment grows by 5% each quarter, write an exponential expression to represent the value of the investment after x quarters if the initial amount was $500.

• $500 * (1.5)^x

• $500 * (1.05)^{x+1}

• $500 * (1.05)^(2x)

• $500 * (1.05)^x

A forest fire spreads to double its size every 6 hours. Write an exponential expression to represent the size of the fire after x hours if it originally covered 10 acres.

• 10 * 2^(x/6)

• 10 * 2^(6/x)

• 10 * 2^(x-6)

• 10 * 2^(x*6)

If a city's population increases by 10% each year, write an exponential expression to represent the population after x years if it originally had 100,000 residents.

• 100,000 * (1.10)^x

• 100,000 + (1.10)^x

• 100,000 * (1.10)^-x

• 100,000 * (1.10)^2x

A bank account earns 3% interest compounded annually. Write an exponential expression to represent the balance after x years if the initial deposit was $2000.

• $2000 * (1 + 0.03)^2x

• $2000 * (1 + 0.03)^{x+1}

• $2000 * (1 + 0.03)^{x-1}

• $2000 * (1 + 0.03)^x