How the number e defined? O The value so that e" at x = 0 is 1. O The value so that e is 10. O The value so that the slope of the tangent line to y = e* at (0, 1) is exactly 1. O The value so that the slope of the tangent line to y = x at (0, 1) is exactly 1. (b) What is an approximate value for e? (Round your answer to five decimal places.) e = (c) What is the natural exponential function? Need Help? Read It 4. [-/5 Points] DETAILS SCALCET9 1.4.015. Starting with the graph of y = ex, write an equation of the graph that results from the following changes. (a) shifting 2 units downward (b) shifting 7 units to the right (c) reflecting about the x-axis y = (d) reflecting about the y-axis (e) reflecting about the x-axis and then about the y-axis5. [-/5 Points] DETAILS SCALCET9 1.4.029.MI. MY NOTES ASK YOUR TEACH A graphing calculator is recommended. A bacterial culture starts with 300 bacteria and doubles in size every half hour. (a) How many bacteria are there after 4 hours? bacteria (b) How many bacteria are there after t hours? bacteria (c) How many bacteria are there after 40 minutes? (Round your answer to the nearest whole number.) bacteria (d) Graph the population function. y 50 000 50 000 50 000 50 000 40 000 40 000 40 000 40 000 30 000 30 000 30 000 30 000 20 000 20 000 20 000 20 000 10 000 10 000 10 000 10 000 O 2 2 3 5 2 3 AO 2 3 4 5 Estimate the time (in hours) for the population to reach 40,000. (Round your answer to one decimal place.) hr6. [-/6 Points] DETAILS SCALCET9 1.4.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A graphing calculator is recommended. Graph the given functions on a common screen. Explain how these graphs are related. y = 2*, y = 10*, v = () . v=(x) The functions with bases greater than 1 (2* and 10*) are [-Select- ~ ] , while those with bases less than 1 ( ) and (1 )|are ---select- ~ ] . The graph of ()" is the reflection of that of 2* about the [? ~ ] -axis, and the graph of ()" is the reflection of that of 10* about the ? v -axis. The graph of 10* increases more quickly than that of 2* for x [? v 0, and approaches 0 faster as ? v ] - -co. Need Help? Read It Watch It