Chapter 4 Section 42 Question 025 In the table below data fo

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=

Solution

(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=ab^x

=>f(x)=ab^x

f(0.00)=2.76

=>a*b^o=2.76

=>a*1=2.76

=>a=2.76

=>f(x)=2.76b^x

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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