Warm-up 1) Identify the following formulas... Exponential Growth Half Life Exponential Decay Compound Interest Standard Form of an Exponential Function

Homework Answers 3) 3.57 millicuries 4a) $4659.98 4b) $1334.05 4c) $157.77

Point-Ratio Form

Point-Ratio Form When you ring a bell or clang a pair of cymbals, the sound seems really loud at first, but the sound becomes more quiet very quickly indicating exponential decay. This sound can be measured in several different ways. The most famous, the decibel, was named after Alexander Graham Bell – inventor of the telephone. We can also use pressure to measure sound. While conducting an experiment with a clock tower bell it was discovered that the sound from that bell had an intensity of 40 lb/in2 four seconds after it rang and 4.7 lb/in2 seven seconds after it rang. 1) Using this information, what would you consider to be the independent and dependent values in the experiment?   2) What two points would be a part of the exponential curve of this data? 3) What was the initial intensity of the sound? 4) Find an equation that would fit this exponential curve.

Point-Ratio Form You can find this equation using exponential regression on your graphing calculator, but what if you don’t have a graphing calculator? You may recall learning how to write equations for linear information using point-slope form. This is a little bit different, obviously, because we’re working with an exponential curve, but when we use point-ratio form, you should see some similarities. Where (x,y) and (x1,y1) are ordered pairs that can be used to find the value of b, the common ratio. OR Where (x1,y1) an ordered pair and the common ratio, b, can be used to write an explicit equation for the scenario or identify other possible values for the scenario.

Now we can answer questions 3 and 4. To find the value of b : To find the initial value: Step 1: Identify two ordered pairs. Step 2: Substitute the values into Point-Ratio Form Step 3: Divide to get the power alone. Step 4: Use the properties of exponents to isolate b. Step 1: Identify two ordered pairs and the b value. Step 2: Substitute the values into Point-Ratio Form Step 3: Substitute 0 for x and simplify (Since the initial value is where x=0)

Find the exponential equation given the points (1, 12. 5) and (3, 3

Practice Problems Carbon-14 decays slowly over several thousand years. When this isotope is formed, there is 50 grams of Carbon-14. Five thousand seven hundred and thirty years later there are 25 grams of Carbon-14. What percentage of the Carbon-14 is lost in 5730 years? What is the initial amount of Carbon-14? Write an equation to represent this situation. Use your equation from part c to predict how much Carbon-14 was present 1000 years after the formation of the isotope.

Practice Problems On old radio dials the numbers are not equally spaced, but they do have an exponential relationship. When the dial is tuned to 88.7 FM, it takes 6 “clicks” to tune to 92.9. Write an exponential model for the radio’s tuning dial if x is the number of clicks past 88.7 and y is the radio station. Show your work. How many clicks would you need to turn the dial past 88.7 to tune to 106.3 FM?

Practice Problems The temperature of a bowl of ice water is measured at 23oC right after ice is added to it. Eight minutes later, its temperature is 14.02oC. Approximately how long will it take for the water to cool to 5oC?

Practice Problems The graph of an exponential function goes through the ordered pairs (-3, 0.32) and (2, 31.25). Write the explicit form of the exponential function. By what percentage are the range values increasing for each increase of 1 in the x-values? (In other words, what is the growth rate?)

Point Ratio Homework 10/20 (1, 3) and (5, 1875) (2,19) and (6, 11)

Homework & Such HW 3-5 Have a Great Day!!