- An investment’s value is rising at the rate of 5% per year. The initial value of the investment is $20,000 in 2016.
- Write the function that gives the value of the investment as a function of time t in years after 2016.
- Find the value of the investment in 2028
- When will the value be $30,000?
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- The population of a city is increasing at the rate of 2.3% per year, since the year 2000. Its population in 2010 was 137,000 people. Find the population of the city in the year 2000.
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- The value of a piece of industrial equipment depreciates after it is purchased. Suppose that the depreciation follows an exponential decay model. The value of the equipment at the end of 8 years is $30,000 and its value has been decreasing at the rate of 7.5% per year. Find the initial value of the equipment when it was purchased.
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- An investment has been losing money. Its value has been decreasing at the rate of 3.2% per year. The initial value of the investment was $75,000 in 2010.
- Write the function that gives the value of the investment as a function of time t in years after 2010.
- If the investment’s value continues to decrease at this rate, find the value of the investment in 2020.
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- A social media site has 275 members initially. The number of members has been increasing exponentially according to the function y=275e0.21t, where t is the number of months since the site’s initial launch. How many months does it take until the site has 5000 members? State answer to the nearest tenth of a month (1 decimal place).
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- A city has a population of 62000 people in the year 2000. Due to high unemployment, the city’s population has been decreasing at the rate of 2% per year. Using this model, find the population of this city in 2016.
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- A city has a population of 87,000 people in the year 2000. The city’s population has been increasing at the rate of 1.5% per year. How many years does it take until the population reaches 100,000 people?
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- An investment of $50,000 is in increasing in value at the rate of 6.3% per year. How many years does it take until the investment is worth $70,000?
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- A city has a population of 50,000 people in the year 2000. The city’s population increases at a constant percentage rate. Fifteen years later, in 2015, the population of this city was 70,000. Find the annual percentage growth rate.
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- 200 mg of a medication is administered to a patient. After 3 hours, only 100 mg remains in the bloodstream. Using an exponential decay model, find the hourly decay rate.
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- An investment is losing money at a constant percentage rate per year. The investment was initially worth $25,000 but is worth only $20,000 after 4 years. Find the percentage rate at which the investment is losing value each year (that is, find the annual decay rate).
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- Using the information in question 11, how many years does it take until the investment is worth only half of its initial value?
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