7.1 EXPONENTIAL FUNCTIONS, GROWTH, AND DECAY Objective Write and evaluate exponential expressions to model growth and decay situations. Vocabulary exponential function base asymptote exponential growth exponential decay Remember! Negative exponents indicate a reciprocal. For example: Warm Up Evaluate. 1. 100(1.08)20 2. 100(1 0.02)10
466.1 81.71 3. 100(1 + 0.08)10 46.32 Growth that doubles every year can be modeled by using a function with a variable as an exponent. This function is known as an exponential function. The graph of the parent function f(x) = 2x is shown. Why not f(x) = 1x as the parent function? Domain: Range:
Look at the graph. What questions come to mind? A function of the form f(x) = abx, with a > 0 and b > 1, is an exponential growth function, which increases as x increases. When 0 < b < 1, the function is called an exponential decay function, which decreases as x increases. Example 1A: Graphing Exponential Functions Tell whether the function shows growth or decay. Then graph. 3 f x 10 4 x Step 1 Find the value of the base.
Step 2 Graph the function by using a table of values. x -1 0 2 4 6 f(x) Highlight your point on the graph
8 10 12 Check It Out! Example 1 Tell whether the function p(x) = 5(1.2x) shows growth or decay. Then graph. Step 1 Find the value of the base. Step 2 Graph the function by using a table of values. x f(x) 12
8 4 Highlight your point on the graph 0 4 8 10 You can model growth or decay by a constant percent increase or decrease with the following formula:
Questions: In the formula, the base of the exponential expression, 1 + r, is called the growth factor. Similarly, 1 r is the decay factor. Example 2: Economics Application Clara invests $5000 in an account that pays 6.25% interest per year. After how many years will her investment be worth $10,000? Step 1 Write a function to model the growth in value of her investment. f(t) = a(1 + r)t Exponential growth function. We will learn algebra techniques for solving. Until then we use the graph or table to solve the equation Example 3: Depreciation Application A city population, which was initially 15,500, has been dropping 3% a
year. Write an exponential function and graph the function. Use the graph to predict when the population will drop below 8000. f(t) = a(1 r)t Exponential decay function. 10,000 0 150
human capacity. and . institutional resource development. for the global application of agriculture and related environmental sciences. OIRED/Virginia Tech - SANREM. ... Works to strengthen networks in the community. Foster farmer-market connections.
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