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Instructions: Interpret the function given in the context of the real-world situation described to answer the question.Suppose a long term investment is modeled by the exponential function V(t)=300(25)t20𝑉(𝑡)=300(25)𝑡20 where V(t)𝑉(𝑡) is the total value after t𝑡 year. What does 300300 represent in the equation?Multiple choice 1 Question 13The interest rateThe growth factorThe initial depositThe number of years

Question

Instructions: Interpret the function given in the context of the real-world situation described to answer the question.Suppose a long term investment is modeled by the exponential function V(t)=300(25)t20𝑉(𝑡)=300(25)𝑡20 where V(t)𝑉(𝑡) is the total value after t𝑡 year. What does 300300 represent in the equation?Multiple choice 1 Question 13The interest rateThe growth factorThe initial depositThe number of years

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Solution

The 300 in the equation represents the initial deposit.

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We have to deal with problem-solving in many real-world situations. Therefore, it is important to know the steps you must take when problem-solving depending on the type of problem. Let's use exponential functions to solve the following problems:Suppose $4000$4000 is invested at a 6%6% interest rate compounded annually. How much money will there be in the bank at the end of five years? At the end of 2020 years?Read the problem and summarize the information.$$ is invested at a %% interest rate compounded annually. We want to know how much money we will have after and after years.Assign variables.x=𝑥= time in yearsy=𝑦= amount of money in the investment account.We start with $4000$4000 and each year we apply a 6%6% interest rate on the amount in the bank. The pattern is that each year we multiply the previous amount by a factor of 100%+6%=106%=1.06100%+6%=106%=1.06. Complete a table of values by continuing to multiply each year’s amount by 1.061.06.

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