Exponential Functions

Exponential Functions

Draw

Write an exponential function.

Multiple Select

Which of the following are exponential functions? Select all correct answers.

• $$f\left(x\right)=4\left(\frac{1}{4}\right)^x$$

• $$g\left(x\right)=14\left(4\right)^x$$

• $$h\left(x\right)=10x^5$$

• $$j\left(x\right)=-9x^4$$

• $$k\left(x\right)=6\left(5.49\right)^x$$

Draw

A population of bacteria is initially 3000. After two hours the population is 1500. If this rate of decay continues, determine the exponential function of the form:

$$f\left(t\right)=a\left(b\right)^{ct}$$

Guided Practice

Multiple Choice

$$Let\ f\left(x\right)=4\left(\frac{1}{3}\right)^{2x}.\ Which\ is\ equal\ to\ f\left(1\right)?$$

• 4/3

• 1/9

• 4/9

• 4/27

• 4/81

Guided Practice

Multiple Choice

$$Which\ function\ contains\ the\ points\ \left(0,\ -4\right)\ and\ \left(2,\ -400\right)?$$

• $$f\left(x\right)=\left(-4\right)^x$$

• $$f\left(x\right)=\left(-10\right)^x$$

• $$f\left(x\right)=4\left(-10\right)^x$$

• $$f\left(x\right)=-4\left(5\right)^x$$

• $$f\left(x\right)=-4\left(10\right)^x$$

Multiple Choice

$$The\ graph\ of\ an\ \exp onenetial\ function\ passes\ through\ \left(1,\ 20\right)\ and\ \left(3,\ 320\right).$$

$$Which\ function\ describes\ the\ function?$$

• $$f\left(x\right)=5\left(2\right)^x$$

• $$f\left(x\right)=2\left(5\right)^x$$

• $$f\left(x\right)=4\left(5\right)^x$$

• $$f\left(x\right)=5\left(4\right)^x$$

• $$f\left(x\right)=10\left(2\right)^x$$

Draw

Write the Compound Interest Formula?

Draw

Write the Continuous Growth/Decay Formula?

Formulas

Continuous Growth/Decay

Compound Interest Formula

Guided Practice

​An amazing PLTL Leader with the name of Brendan has $10,000 (in his dreams). If he has a savings account that earns 12% interest compounded semiannually, How much money would he have after 5 years?

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Myra invested $10,000 in an account waring a nominal 8% per year compounded continuosly. How much was in the account at the end of one year? Round to the nearest dollar.

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Bill is saving for his son's college education. If the savings account earns 5% interest compounded monthly, and he wants to have $45,000 in 10 years, what must the principal be?

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Matt purchased a new car for $30,000. The car depriciates approximately 12% of its value each year compounded continuosly. How much is it worth after 5 years? Round the answer to nearest dollar.

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A radioactive substance has a decay rate of 0.079 per minute. How many grams of a 200 gram sample will remain radiactive after 1 hour. Round the answer to the nearest tenth of a gram.

HINT: Use the Continuous Growth/Decay Formula.

Good Job!