Exponentials and Logarithms Word Problems

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

Tags

CCSS.HSF.LE.A.2

Due to its weakening steel industry, Canalave Town has been experiencing a population decline of 10% every year. The current population is 74,000 people. Assuming the trend continues, which equation projects the population in x years?

• y = 74,000 (0.10)^x

• y = 74,000 (0.90)^x

• y = 74,000 (1.10)^x

• y = 74,000 (1.90)^x

Tags

CCSS.HSF.LE.A.2

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

A city doubles its size every 64 years. If the population is currently 225,000, what will the population be in 128 years?

• The population will be 225,000.

• The population will be 450,000.

• The population will be 900,000.

• The population will be 1,800,000.

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

ON

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AI.9.9.C

If the population of a city is 50,000 and grows at a continuous rate of 3% per year, what will be the population after 5 years?

• 58,091

• 55,000

• 60,000

• 50,000

The equation Q = 12e^{-.09t is given to show the amount of an element remaining after t years. how long will it take for the element to reach 3 mg?}

• 4.5 years

• 12.7 years

• 2.7 years

• 15.4 years

Using logarithms to solve real-world problems: The value of a car depreciates by 10% each year. If the initial value of the car is $20,000, what will be its value after 5 years?

• The value of the car after 5 years will be $25,000.

• The value of the car after 5 years will be $18,000.

• The value of the car after 5 years will be $12,861.30.

• The value of the car after 5 years will be $22,000.

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

Tags

CCSS.HSF.LE.A.2

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.

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CCSS.HSF-LE.A.1C