Unit 4 Exponential Functions and Equations Expressions and Equations Lesson 13 Exponential Functions with Base e ALGEBRA 2 e on a Calculator Warm-up The other day, you learned that e is a mathematical constant whose value is approximately 2.718. When working on problems that involve e, we often rely on calculators to estimate values. 1. Find the e button on your calculator. Experiment with it to understand how it works. (For example, see how the value of 2e or e2 can be calculated.) 2. Evaluate each expression. Make sure your calculator gives the indicated value. If it doesn’t, check in with your partner to compare how you entered the expression. a. 10 ⦁ e(1.1) should give approximately 30.04166 b. 5 ⦁ e(1.1)(7) should give approximately 11,041.73996 c. e9/23 + 7 should give approximately 8.47891 Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics. Same Situation, Diﬀerent Equations The population of a colony of insects is 9 thousand when it was ﬁrst being studied. Here are two functions that could be used to model the growth of the colony months after the study began. P(t) = 9 ⦁ (1.02)t Q(t) = 9 ⦁ e(0.02t) 1. Use technology to ﬁnd the population of the colony at diﬀerent times after the beginning of the study and complete the table. 2. What do you notice about the populations in the two models? Same Situation, Diﬀerent Equations 3. Here are pairs of equations representing the populations, in thousands, of four other insect colonies in a research lab. The initial population of each colony is 10 thousand and they are growing exponentially. is time, in months, since the study began. a. b. Colony 1 f(t) = 10 ⦁ (1.05)t g(t) = 10 ⦁ e(0.05t) Colony 2 k(t) = 10 ⦁ (1.03)t l(t) = 10 ⦁ e(0.03t) Colony 3 p(t) = 10 ⦁ (1.01)t q(t) = 10 ⦁ e(0.01t) Colony 4 v(t) = 10 ⦁ (1.005)t w(t) = 10 ⦁ e(0.005t) Graph each pair of functions on the same coordinate plane. Adjust the graphing window to the following boundaries to start: 0 < x < 50 and 0 < y < 80. What do you notice about the graph of the equation written using and the counterpart written without ? Make a couple of observations.

Unit 4 - Exponential Functions and Equations

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