University:
Carleton College
Course:
MATH 120 | Calculus 2
Academic year:

2024
Views:

91

Pages:

3
Author:

Nevaeh Bauer

Question 1 What is the square root of 300 in radical form? Answer 1 Step 1 First see if 300 has any perfect squares as factors. 4 divides 300 giving 75, so there's one. 25 divides 75 giving 3, so there's a second. 3 is'. So, √300 = √4 x 25 x √3 = 2 x 5 x √3 = 10√3 That's the answer. We could also note that 300 = 3 x 100, so its square root is √3√100 = 10√3. Answer 2 Step 1 I'm assuming you want the principal square root, which is simply: √300 = √100 × √3 = 10√3 Answer: 10√3 If you wanted the other square root, it's -10√3 Question 2 Write the radical expression using exponents and each exponential expression using radicals. √7^3 Answer Step 1 The given expression is √7^3 Radical rule: ⁿ√aᵐ = a^m/n Exponent rule: (a^m)^n = a^mn Step 2 √7^3 = (7^3)^1/2 = 7^3/2 Question 3 Use a graphing calculator to determine the exponential regression equation to model the relationship between the decades since 1950 and the population. a. The calculator returns two values, a and b. Write these values below. Round a to the nearest whole number and b to the nearest thousandth, if necessary. a =?, b =?. b. The general form of an exponential function is y = ab^x. b. The general form of an exponential function is y = ab^x. Use this general form and the values of a and b from Part (a) to write an exponential function that models Nevada's population growth. c. Use a graphing calculator to graph the data points and the function from Part (b). Sketch the graph and the data points below. Is the exponential function a good approximation of the data? Explain. Answer Step 1 a. Values of a and b a = 182,753 and b = 1.612 b. Function The exponential function that represents the population growth of Nevada f(x) = 182, 753 * (1.612)^x Step 2 c. Graph of the data blue - graph of the function orange - graph of the data points The exponential function is a good approximation of the data as shown on the graph since the graph of the function is closer to the graph of the data points. Question 4 Rewrite the expression using rational exponents. ³√x² Answer Step 1 Given radical expression: ³√x² Step 2 To write Radicals as Exponents: ⁿ√xᵐ = x^m/n Therefore, ³√x² = x^2/3 Hence, the radical expression ³√x² is written in rational exponents as x^2/3 Question 5 To simplify the expression (-27)^(1/3) Answer Step 1 According to the power rule (b^n)^m = b^(n*m) Given expression is (-27)^(1/3) This can be written as (−27)^(1/3) = {(-3) × (-3) × (-3)}^(1/3) (−27)^(1/3) = {(-3)³}^(1/3) Applying the power rule, (−27)^(1/3) = {(-3)}^(3×1/3) (-27)^(1/3) = (-3)