Presentation on theme: "4-1:Exponential Growth and Decay"— Presentation transcript:
14-1:Exponential Growth and Decay English CasbarroUnit 4
2Exponential Functions If an output doubles every year, it can be modeled by an exponential functionThe parent function is: f(x) = bx, where b is a constant and x is the independent variable.b > 0, and b ≠ 1
3Remember the graph on the introduction: y = 2x 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.
4b is the constant of growth if b > 1 The standard form of an exponential growth (decay) function:a is the initial amountb is the constant of growth if b > 1b is the constant of decay if 0< b < 1x is usually the time
5For exponential growth, as the value of x increases, the value of y increases. For exponential decay, as the valueof x increases, the value of y decreases, approaching zero.
7You can model growth or decay by a constant percent increase or decrease withthe following formula:Number of time periodsFinal amountInitial amountRate of growth or decayIn the formula, the base of the exponentialexpression 1 + r, is called the growth factor.Similarly, 1 – r is called the decay factor.
13Turn in the following problems 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 isthe 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 paid5% interest compounded monthly (12 times per year). How much more wouldhis investment have been worth after 5 years?2. What are the values of a and b in f(x) = abx in the graphshown at the right?3. The population of Midland, Texas was 89, 443 in 1990and has increased at a rate of 0.6% per year since then.Which function represents the Midland’s growth functionafter t years?89,443(1.6)t B. 89,443(1.06)tC. 89,443(1.006)t D. 89,443(1.0006)t