The basic growth/decay exponential model is A(t) = A br. The predicted future value of a...

  

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The basic growth/decay exponential model is A(t) = A br. The predicted future value of a commercial property in $ millions is a function of time, t, in years from 2020 is given by A(t) = 5 (1.14) Interpret this function. Is this a growth or decay model? What is the current value of this property? By what percentage is the value of this function increasing or decreasing on what time interval? 3. Graph and Analyze an Exponential Function Progress is being made on the incidence of measles in an African country, as a result of an accessible vaccination program. The number of diagnosed cases in thousands as a function of time, t, in years from 2016 is given by N(t) = 16(21)-1 a) Inspect the function and explain why this equation represents a decreasing function: b) State the equation of the horizontal asymptote: c) Find the intercepts. Use the One-to-One Property of Exponentiation to find the t-intercept. Clearly show your algebra steps. Verify the intercepts using DESMOS. Find N-intercept: Find t-intercept: What is the meaning of this intercept in the problem context? What is the meaning of this intercept in the problem context? d) State the practical domain and range of this function in interval notation: Practical domain: Practical range: 1. Analyze and Interpret a Rational Function The effluent from a gold mine is being filtered to reduce the particulate concentration of a toxic heavy metal to a safe level. The function, C(x), represents the pollutant concentration in ppm as a function of the number of filters that the effluent must pass through, x. 2x x-5 C(x): = x+3 x+2 a) Simplify the right side to a single fraction: Graph this function using DESMOS. Do not include the DESMOS graph here. b) State the equations of the Vertical Asymptotes: State the mathematical domain of this function in interval notation: State the practical domain of this function in interval notation: c) Is this function a Case 1 or 2 Rational Function? State the equation of the Horizontal Asymptote: d) Which asymptote is relevant in the problem context? Explain the significance of this asymptote in this problem context: The basic growth/decay exponential model is A(t) = A br. The predicted future value of a commercial property in $ millions is a function of time, t, in years from 2020 is given by A(t) = 5 (1.14) Interpret this function. Is this a growth or decay model? What is the current value of this property? By what percentage is the value of this function increasing or decreasing on what time interval? 3. Graph and Analyze an Exponential Function Progress is being made on the incidence of measles in an African country, as a result of an accessible vaccination program. The number of diagnosed cases in thousands as a function of time, t, in years from 2016 is given by N(t) = 16(21)-1 a) Inspect the function and explain why this equation represents a decreasing function: b) State the equation of the horizontal asymptote: c) Find the intercepts. Use the One-to-One Property of Exponentiation to find the t-intercept. Clearly show your algebra steps. Verify the intercepts using DESMOS. Find N-intercept: Find t-intercept: What is the meaning of this intercept in the problem context? What is the meaning of this intercept in the problem context? d) State the practical domain and range of this function in interval notation: Practical domain: Practical range: 1. Analyze and Interpret a Rational Function The effluent from a gold mine is being filtered to reduce the particulate concentration of a toxic heavy metal to a safe level. The function, C(x), represents the pollutant concentration in ppm as a function of the number of filters that the effluent must pass through, x. 2x x-5 C(x): = x+3 x+2 a) Simplify the right side to a single fraction: Graph this function using DESMOS. Do not include the DESMOS graph here. b) State the equations of the Vertical Asymptotes: State the mathematical domain of this function in interval notation: State the practical domain of this function in interval notation: c) Is this function a Case 1 or 2 Rational Function? State the equation of the Horizontal Asymptote: d) Which asymptote is relevant in the problem context? Explain the significance of this asymptote in this problem context: