Question

9. A population of bears decreases exponentially. 400 a. What is the annual factor of decrease for the bear population? Explain how you know. 300 bear population 200 100 b. Using function notation, represent the relationship between the bear population, b, and the number of years since the population was first measured. I. That is, find a function, . so that b = f(t). 2 3 4 5 years since 2010 (From Unit 5, Lesson 8.) 10. Equations defining functions ab.c.d. and are shown here. Select all the equations that represent exponential functions. A. a(x) = 2x B. b() = (?) Ccm) = 2" D. dx) = 32 E. (t) = 3.2

Answer 1

9a. 0.8

9b. f(t) = 400(0.8^t)

10. B, C, E

Explanation:

The growth factor (or factor of decrease) for a time period will be found by taking the ratio of the value at the end of the time period to the beginning value.

9a.

The population is 320 after 1 year. It started at 400 at the beginning of the year, so the factor of decrease is 320/400 = 0.80.

b.

The exponential function can be written as ...

f(t) = a·b^t . . . . . where 'a' is the initial population, and 'b' is the factor of decrease

The initial population is shown on the graph as 400; the factor of decrease is what we just computed.

f(t) = 400(0.80^t)

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10.

An exponential function is one that has the independent variable as an exponent. That form is seen in selections B, C, E.