5a) Which describes how the graph of f can be obtained from the graph of y = ex ? Select one answer. A. B. C. D. Shift the graph of y = ex to the left by 1 unit and up by 4 units. Shift the graph of y = ex to the right by 1 unit and up by 4 units. Reflect the graph of y = ex across the x-axis and shift up by 4 units. Reflect the graph of y = ex across the y-axis and shift up by 4 units. (b) What is the domain of f ? (c) What is the range of f ? (d) What is the horizontal asymptote? (e) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth). 6. (10 pts) Exponential Regression (Section 6.5) Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically, in Table 1. TABLE 1 t = Time Elapsed (minutes) 0 10 20 30 40 50 60 C = Coffee Temperature (degrees F.) 166.0 140.5 125.2 110.3 104.5 98.4 93.9 REMARKS: Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach the ambient temperature of the room, 69 degrees. So, the temperature difference between the coffee temperature and the room temperature will decrease to 0. We will fit the temperature difference data (Table 2) to an exponential curve of the form y = A ebt. Notice that as t gets large, y will get closer and closer to 0, which is what the temperature difference will do. So, we want to analyze the data where t = time elapsed and y = C 69, the temperature difference between the coffee temperature and the room temperature. TABLE 2 t = Time Elapsed (minutes) 0 10 20 30 40 50 60 y = C 69 Temperature Difference (degrees F.) 97.0 71.5 56.2 41.3 35.5 29.4 24.9 The exponential function of \"best fit\" (using the data in Table 2) is shown below: y = 89.976 e 0.023 t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees) (a) Use the exponential function to estimate the temperature difference y when 35 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. Show work. (b) How long will it take for the coffee to reach a temperature of 120 degrees? HINT: We first must find the value of y, which is C - 69. Therefore, y = 120 - 69 = 51. We now use this value of y=51 in the equation and then solve for t = time. Don't forget to follow the rules on solving an exponential equation. You are solving: 51 = 89.976 e 0.023 t 7. (10 points) Express the following terms as a single equivalent logarithmic expression. Show work. log 1 + log (x) - 2 log (y+2) 8. (10 points) Solve the following exponential equation. Show work. 22 x+1 =8