Pre-AP Precalculus



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3.1 Exponential Functions and Their Graphs

Definition of Exponential Function

The exponential function f with base a is denoted by f(x) = ax,

where a > 0, a[pic]1, and x is any real number.

Use a calculator to evaluate each function at the indicated value of x.

1) f(x) = 8x x = [pic] 2) f(x) = 8-x x = ½ 3) f(x) = 0.8x x = -2.5

Graphs of Exponential Functions

4) y = 2x 5) y = 2-x 6) y = 5x 7) y = 5-x

Graphs of y = ax Graphs of y = a-x

Domain: Domain:

Range: Range:

Intercept: Intercept:

Increasing or Decreasing Increasing or Decreasing

Horizontal Asymptote: Horizontal Asymptote:

Graph the following functions. Describe the transformation that occurred

Parent Function: [pic]

8) [pic]

9)[pic]

10) [pic]

11) [pic]

Transformations of Graphs of Exponential Functions

Describe the graphs as a transformation of the graph of f(x) = 4x.

12) g(x) = 4x-2 13) h(x) = [pic] 14) q(x) = 4-x + 3

Solve for x.

15) 16 = 2x+2 16) [pic] 17) [pic]

The Natural Base e e[pic]2.718281828……

The Natural Exponential Function f(x) = ex

Use a calculator to evaluate the function given by f(x) = ex at each individual value of x to four decimal places.

18) x = 6.2 19) x = -0.4 20) x = -7.1 21) x = 0.72

Graph the given function and describe the graphs as a transformation of the graph of f(x) = ex.

22) g(x) = 5ex 23) h(x) = e2x – 3 24) q(x) = -2ex+3

[pic]

Exponential Growth Exponential Decay

[pic] [pic]

25) A species of rabbits in increasing at a rate of 7% per year. If there are currently 10,000 rabbits, how many will there be in 15 years?

26) A home in Frisco is currently worth $150,000. If homes in Frisco are appreciating at a rate of 2.4% per year, when will the home be worth $200,000?

27) If you buy a new car for $25,000 and cars depreciate at a rate of about 8% per year, how much could you sell it for in 5 years?

Compounded Interest A = [pic]

Continuously Compounded Interest A = Pert

20) On the day of a child’s birth, a deposit of $25,000 is made in a trust fund that pays 8.25% interest. Determine the balance in this account on the child’s 26th birthday if the interest is compounded a) quarterly, b) monthly, and c) continuously.

21) Let Q represent the mass of radium (226Ra) whose half-life is 1620 years. The quantity of radium present after t years is given by [pic].

a) Determine the initial quantity (when t = 0).

b) Determine the quantity present after 1000 years.

22) The number V of computers infected by a computer virus increases according to the model V(t) = 100e4.6052t, where t is the time in hours. Find the number of computers infected in

a) 1 hour b) 1.5 hours and c) 2 hours.

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