MAT 105 UNIT 3 MILESTONE 3 (Strayer University)

Solve for x in the following equation:  x = -9  x = 6  x = 9  x = -6 RATIONALE The first step to solve an exponential equation using the base is to create an expression with the same base so that you can solve for x in the exponents. You can change the second half of the equation to have a base of 3. Finally, you can set the exponents equal to each other. CONCEPT Solving an Exponential Equation Using the Base Report an issue with this question 2 Asher owns a square plot of land. He knows that the area of the plot is between 4200 and 4300 square meters. Which of the following is a possible value for the side length of the plot of land?  85 meters  30 meters  100 meters  65 meters RATIONALE Asher owns a plot of land that is perfectly square. The area of the plot is between 4200 and 4300 square meters. One way to solve this problem is to find the area for each side length given. The area of a square is a special case in which the length and the width are the same, so you can find the area by squaring the length. If the side length of the square is 45 meters, then the area equals 2025 square meters. This is NOT a possible length for Asher’s plot because 2025 is not between 4200 and 4300. If the side length of the square is 55 meters, then the area equals 3025 square meters. This is NOT a possible length for Asher’s plot because 3025 is not between 4200 and 4300. If the side length of the square is 75 meters, then the area equals 5625 square meters. This is NOT a possible length for Asher’s plot because 5625 is not between 4200 and 4300. If the side length of the square is 65 meters, then the area equals 4225 square meters. This is a possible length for Asher’s plot because 4225 is between 4200 and 4300. CONCEPT Comparing Area Measures Report an issue with this question 3 Otis monitors the number of strep infections reported in a certain neighborhood each week. According to his reports, infections are growing at a rate of 28% per week. If the number of infections starts at 8 and continues to grow exponentially, what will the number of infections be in week 7?  31 infections  45 infections  38 infections  26 infections RATIONALE Exponential growth can be expressed with the formula . Plug in 8 for a, the initial value, 0.28 for b, the growth rate, and 7 for x, the time: