Chapter 4, Section 4.2, Question 025 In the table below, data for the functions

Question

Chapter 4, Section 4.2, Question 025 In the table below, data for the functions f, g, and h are given rounded to the nearest 0.01. One of them is linear, one is exponential, and one is neither. x 0.00 3.00 6.009.00 12.00 f (x) 2.76 2.933. 3.30 3.50 g 2.76 457 5.79 6.3 6.65 h(x) 2.76 4.055.34 6.63 7.9 (a) Which function is linear, and which is exponential? is linear. is exponential. (b) Find a formula for the exponential function in the form y = alt. Enter your formula and the values for a and b below. Round any values to two decimal places, if required. a=

Explanation / Answer

(a)

h(x) has constant slope

slope =(4.05-2.76)/(3-0) =0.43

so h(x) is linear

f(x) has constant 3unit growth factor

3unit growth factor =(2.93/2.76)=1.0615942

f(x) is exponential

g(x) is neither

(b)

y=abx

=>f(x)=abx

f(0.00)=2.76

=>a*bo=2.76

=>a*1=2.76

=>a=2.76

=>f(x)=2.76bx

f(3.00)=2.93

=>2.76b3=2.93

=>b=(2.93/2.76)1/3

=>b=1.02

f(x)=2.76*(1.02)x

=>y=2.76*(1.02)x

a=2.76

b=1.02

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