5 2 Exponential Functions Objectives Graph identify transformations

5. 2 Exponential Functions Objectives: Graph & identify transformations of exponential functions. 2. Use exponential functions to solve application problems. 1.

Exponential Functions � � �

Example #1 Translations A. Translated right 4 units. B. Translated up 5 units. C. Translated left 2 units & down 3 units.

Example #2 Reflections A. Reflected over the y-axis. B. Reflected over the x-axis. C. Reflected over the x-axis & y-axis.

Example #3 Average Rate of Change � Find the average rate of change for the given function. � Remember to find the average rate of change use:

Example #4 Difference Quotient �Find the difference quotient for the given function. Remember to find the difference quotient use: This expression cannot be simplified.

Example #5 Finance Application If you invest $5000 in a stock that is increasing in value at the rate of 3% per year, then the value of your stock is given by the function with x measured in years: A. Assuming that the value of your stock continues growing at this rate, how much will your investment be worth in 4 years?

Example #5 Finance Application B. When will your investment be worth $8000? Use a graphing calculator and the intersection method to solve this equation. Use ZOOM 0: Zoom. Fit & ZOOM 3: Zoom Out (ENTER) To fit the lines on the screen. Use 2 nd TRACE (CALC) 5: intersect Followed by ENTER three times to find the intersection point. The investment will reach $8000 in 15. 9 years.

Example #6 Population Growth � The projected population of Tokyo, Japan, in millions, from 2000 to 2015 can be approximated by the function where x = 0 corresponds to the year 2000: A. Estimate the population of Tokyo in 2015. x = 2015 – 2000 = 15 The population will be about 27. 2 million.

Example #6 Population Growth B. If the population continues to grow at this same rate after 2015, in what year will the population reach 30 million? Remember it may be necessary to reset your zoom to the default and then going through the same process as before. ZOOM 6: Zstandard This problem may need zoomed out twice. 2000 + 67 = 2067

Example #7 Logistic Model � The population of certain bacteria in a beaker at time t hours is given by the following function. Graph the function and find the upper limit on the bacteria population. Graph the function on the Y = screen. Adjust the zoom just like on the previous examples. What we are looks for is the upper limit of the function as we go further and further to the right. By pressing TRACE and scrolling right with the cursor it appears that the upper limit is 100, 000.