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Answer: The growth factor is 1 5. The function y = h(x) is an exponential function that has the value 7 at x = 0 and grows by the factor of 10 when x is increased by 4. Give a formula for it. Radium-226 has a half-life of 1620 years. If a sample has a mass of 4 grams now, what will its mass be in 1620 years? In 3240 years? In 5000 years?
You can use a graphing calculator to evaluate an exponential function. For example, consider the exponential function f (x) 2x. ( −3.1) 2–3.1 = ( 2 ) 22/3. Work with a partner. Match each exponential function with its graph. Use a table of values to sketch the graph of the function, if necessary. Work with a partner.
An exponential function f with base b is defined by f ( or x) = b x y = b x , where b > 0, b ≠ 1, and x is any real number. Note: Any transformation of y = b x is also an exponential function.
As x increases by 1, y is multiplied by 2. So, the function is exponential. Evaluate each function for the given value of x. Write the function. Substitute for x. Evaluate the power.
Exponential Functions In this chapter, a will always be a positive number. For any positive number a>0, there is a function f : R ! (0,1)called an exponential function that is defined as f(x)=ax. For example, f(x)=3x is an exponential function, and g(x)=(4 17) x is an exponential function.
EXPONENTIAL FUNCTIONS 2 From Table 2 we can infer that for these two functions, exponential growth dwarfs linear growth. • Exponential growth refers to the original value from the range increases by the same percentage over equal increments found in the domain.
Exponential functions are functions like f(x) xa, where the base a is a fixed number and the index is given different values. When a!1 the function increases rapidly as x increases, and when a 1 the function decreases rapidly as x increases. Example (a) x 0 1 2 3 4 5 6 7 8 2x 1 2 4 8 16 32 64 128 256 100 (b) x 0 1 2 3 4 5 6 7
