Exponential Functions Section 1.3. Exponential Functions What real-world situations can be modeled with exponential functions???

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Presentation transcript:

Exponential Functions Section 1.3

Exponential Functions What real-world situations can be modeled with exponential functions???

Rules for Exponents

The Number e

Basic Practice Problems Graph the function. State its domain, range, and intercepts. y-int: x-int:

Basic Practice Problems Rewrite the exponential expression to have the indicated base. base 2 base 5

Basic Practice Problems Solve the given equations graphically. Did you remember to sketch your graphs? No solution! Multiple correct graphs for the second one?

Application Problems The population of Flagstaff was 58,154 in 2005, and assume that the population is growing exponentially at a rate of 0.24% annually. What was the population in 2012? Approximately when (in what year) will the population be 70,000? Hint: Let t represent the number of years since 2005 The model: people Solve graphically: According to this model, the population of Flagstaff will reach 70,000 in the year 2082.

Application Problems The half-life of the radioactive element Proctorium-34 is 39 days. If Proctor needs at least 1 gram of the element to properly teach calculus, and he has 892 grams on the first day of school, for how long will he be able to teach calculus? The model: Solve graphically: Proctor will be able to teach calculus through the end of the school year!!!

Application Problems Determine how much time is required for an investment to triple in value if interest is earned at the rate of 6.1% compounded quarterly. Do you remember the equation for compound interest? In this case, we want to solve: years

Application Problems Determine how much time is required for an investment to quadruple in value if interest is earned at the rate of 8.719% compounded continuously. Do you remember the equation for continuous compounding? In this case, we want to solve: years