The values of two functions, fand g, are given in a table. One, both, or neither
ID: 2885315 • Letter: T
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The values of two functions, fand g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. HINT [See Example 1.] (If an answer does not exist, enter DNE.) calcPac f(x) 0.5 1.54.5 13.5 40.5 +-Operations Functions g(x) 12 6 1.5 0.75 Rclations n0 a(x)- Sets o!Vectors Need Help? Read it-L Practic elt?1Talktoa Tutori Greek Submit Answer Save Progress Practice Another Version . 0.5/1 points| Previous Answers WancFMACS 9.2.020 My Notes Ask Your The values of two functions, fand g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. HINT [See Example 1.] (If an answer does not exist, enter DNE.) -2-0 f(x) 15 3 6 12 24 g(x) f(x)dne g(x) -dne Need Help? Read itthPraticeiTak to a TutorExplanation / Answer
6)
Let f(x) is an increasing function. f(x)=ae^(bx)
x=-2. f(x)=0.5
Then 0.5=ae^(-2b) --------(1)
x=-1. f(x)=1.5
Then . 1.5=ae^(-b) . ---------(2)
(2)/(1) .--->. Is 3=e^b
b=ln(3)=1.0986123
By solving eq(2)--->. a=4.5
f(x)=4.5e^(1.0986123x) . Answer
Solve for g(x)
It's decreasing function g(x)=ae^(bx)
x=-2. g(x)=12
12=ae^(-2b). ---------(1)
x=-1. g(x)=6
6=ae^(-b) -----------(2)
Solving eq(2)/eq(1)------> 0.5=e^b
b=ln(0.5)= -0.6931472
from eq(2) -----> a=3
g(x)=3e^(-0.6931472x) Answer
7)
f(x) is an increasing function
Let f(x)=ae^(bx)
x=-2. f(x)=1.5
Then 1.5=ae^(-2b) ---------(1)
x=-1 f(x)=3
Then. 3=ae^(-b) . -----------(2)
(2)/(1)----->. 2=e^b
b=ln(2)=0.6931472
by solving eq(2)--> 3=ae^(-0.6931472)
a=6
f(x)=6e^(0.6931471x). Answer
g(x) is not exponential model when x tends to infinity only then function is zero but from given data when x=-1 or +1 then function defined is zero so doesn't exist . DNE
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