Presentation on theme: "4-1:Exponential Growth and Decay English Casbarro Unit 4."— Presentation transcript:
4-1:Exponential Growth and Decay English Casbarro Unit 4
Exponential Functions If an output doubles every year, it can be modeled by an exponential function The parent function is: f(x) = b x, where b is a constant and x is the independent variable. b > 0, and b ≠ 1
Remember the graph on the introduction: y = 2 x Notice that as x decreases, the graph gets closer and closer to the x-axis. The graph, however, will never touch the x-axis, so it is an asymptote.
The standard form of an exponential growth (decay) function: a is the initial amount b is the constant of growth if b > 1 b is the constant of decay if 0< b < 1 x is usually the time
For exponential growth, as the value of x increases, the value of y increases. For exponential decay, as the value of x increases, the value of y decreases, approaching zero.
You can model growth or decay by a constant percent increase or decrease with the following formula: Final amount Initial amount Rate of growth or decay Number of time periods In the formula, the base of the exponential expression 1 + r, is called the growth factor. Similarly, 1 – r is called the decay factor.
The value of a truck bought new for $28,000 decreases 9.5% each year. Write an exponential function, and graph the function. Use the graph to Predict when the value will fall to $5000.
Transformation of the graph
Turn in the following problems 1.The compound interest formula is, where A is the amount earned, P is the principal, r is the annual interest rate, t is the time in years, and n is the number of compounding periods per year. Harry invested $5000 at 5% interest compounded quarterly(4 times per year). a. How much will the investment be worth after 5 years? b. When will the investment be worth more than $10,000? c. What if Harry could have invested the same amount in an account that paid 5% interest compounded monthly (12 times per year). How much more would his investment have been worth after 5 years? 2. What are the values of a and b in f(x) = ab x in the graph shown at the right? 3. The population of Midland, Texas was 89, 443 in 1990 and has increased at a rate of 0.6% per year since then. Which function represents the Midland’s growth function after t years? A.89,443(1.6) t B. 89,443(1.06) t C. 89,443(1.006) t D. 89,443(1.0006) t