Applications of Exponential

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

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

• 29 to 30 years

• 23 to 24years

• 15 to 16 years

• 19 to 20 years

You drink a beverage with 120 mg of caffeine. The caffeine in your system decreases continuously by about 12% per hour. How long until you have 10mg of caffeine? 

• 20 to 21 hours

• 18 to 19 hours

• 15 to 16 hours

• 5 to 6 hours

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x

• y=1.09(1400)^x

• y=1400(.91)^x

• y=1.09^x

You drink a Coca-Cola with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 15mg of caffeine? 

• 16 hours

• 17 hours

• 18 hours

• 19 hours

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x

• y=15,000(0.92)^x

• y=15,000(1.08)^x

• y=15,000(0.08)^x

The population of Boringtown decreased annually by 1.8% between the year 2015-2018. In 2015, there were approximately 200,000 people living in Boringtown. Which function models the city's population since 2015?

• f(x) = 200,000(1 + 0.018)³

• f(x) = 200,000(1 - 0.18)³

• f(x) = 200,000(1 + 0.18)³

• f(x) = 200,000(1 - 0.018)³

Identify the percent (%) increase or decrease for the function below:

f(x) = 3000 (1.17)^x

• Increase by 0.17%

• Increase by 17%

• Decrease by 17%

• Decrease by 0.17%

Write the function for the info below. Initial Value: 25,000 Decay: Decrease by 5%

• f(x)=0.05(25,000)^x

• f(x) = 0.95(25,000)^x

• f(x) = 25,000 (0.95)^x

• f(x) = 25,000 (1.05)^x

Jimmy purchased a rare coin for $350. It will appreciate (increase) in value by about 6% each year. Write the equation that represents this.

• f(x)=350(0.06)^x

• f(x)=0.06(350)^x

• f(x)=350(1 - 0.06)^x

• f(x)=350(1 + 0.06)^x