University:
Morehouse College
Course:
HMTH 105 | College Algebra 1
Academic year:

2024
Views:

407

Pages:

2
Author:

Reynaldo Wong

Question 1 The loudness 1(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 * log(x/10) where l_{0} = 10 ^ - 10 watt per square meter is the least intense sound ear can detectedDetermine the loudness, in decibels, of each of the following sounds. Heavy city traffic: intensity of x = 10 ^ - 3 watt per square meter. Answer 1 It is observed that the loudness is a logarithmic function. Hence, the different properties of logarithmic function can be used to find the find the intensity. The different properties of the logarithmic function are found from the properties of the exponential functions as exponential functions are inverse functions of logarithmic functions. Now, to find the intensity at x = 10 ^ - 1 watt per sq meter, substitute this value in the loudness function given by L(x). The logarithmic properties log(x ^ n) = n * log(x) and log(10) = 1c can be used simplify the equation. L(x) = 10 * log(x/10) L(10 ^ - 3) = 10 * log((30 ^ - 4)/10) = 10 * log(10 ^ - 2) = - 2 * 10 * log(10 ^ - 4) = - 2 * 10 * log(10) -20 dB Question 2 When a and bly abx models negative exponential growth. a. Write an exponential function that models negative growth. b. Give an example of a situation that could be modeled by your function. c. Explain one difference between negative exponential growth and exponential decay. Answer 1 18000 = P * e ^ 0 * (4) A-Pet 28000=P(127124915) Solve for 21 3P = 6, 293.02 Divide 8000 by 1.27124915 Question 3 Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data. If it is exponential, find an exponential function that models the data x f(x) -18/708156 2 392 Answer 1 The function is linear if there is a common difference between the y-values for a constant increase in the z-values while the function is exponential if there is a common ratio between the y-values for a constant increase in the z-values. Since there is a common ratio of 7 between the y-values for constant increase of 1 in the x-values, then the function is exponential. Use the exponential model y ab where a is the initial value (where x=0) and & is the common ratio. Substitute a = 8 and b= 7 so: y = 8(7) or f(x) = 8(7) Question 4 How do you tell which function-linear, exponential, or quadratic-best represents data? Answer 1 A linear model will likely fit well if the first differences between consecutive y-values are constant or very close to constant If the Ist differences are not constant then use those numbers to find the 2nd differences. If they are constant or nearly constant then a quadratic model will probably fit well/ If the ratios of consecutive y values are constant or very nearly constant then an exponential model will likely work well. Question 5 How can you tell if an exponential function models growth or decay? Answer 1 An exponential function of the form y=a*b^x is an exponential growth function is bel and an exponential decay function is 0