SOLUTION: Refer to the economic loss index function below. The economic loss index in terms of x days of life is modeled by the formula: f(x)= 0.41 ln(x+1) +28 a. evaluate f(0) and f(100).

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Question 1040389: Refer to the economic loss index function below. The economic loss index in terms of x days of life is modeled by the formula:
f(x)= 0.41 ln(x+1) +28
a. evaluate f(0) and f(100).
b. How many days does it take the economic loss index to be 31?
if you could please a step by step answer with some notes on the side i would greatly appreciate it.
Thank you
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
f(x)= 0.41 ln(x+1) +28
f(0)=0.41* ln(1)+28, because x+1=1.
ln(1)=0
Therefore f(0)=28
f(100)=0.41*ln(101)+28
ln(101)=4.615
Without rounding yet, multiply that by 0.41, then add 28. Then round
The first part is 1.892, and the answer is 29.892 to three places.
f(x)=31
31=0.41*ln(x+1)+28. Subtract 28 from both sides
3=0.41*ln(x+1), divide both sides by 0.41
7.317=ln(x+1). Don't round. Now, raise both sides to the e power. e ^ ln (x+1)=x=1 by definition.
e^7.37=x+1
1505.79=x+1
to the nearest day, x=1504.79 or 1505 days
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Check
0.41 ln (1506)+28; ln (1506)=7.317
7.317(0.41)=3.000
3+28=31