Let f(x)=24/1+3e−1.3x .
2 answers:
Answer:
(ln(3)/1.3, ∞)
Step-by-step explanation:
The growth rate of the function is given by the first derivative:
f'(x) = -93.6e^(-1.3x)/(1 +3e^(-1.3x))^2
The interval on which this is decreasing can be found by looking at the second derivative:
f''(x) = -93.6(1.3e^(-1.3x)(1+3e^(-1.3x))^-2 -e^(-1.3x)(-2)(3)(-1.3)e^(-1.3x)(1+3e^(-1.3x))^-3)
This will be zero when ...
-3e^(-1.3x) +1 = 0 . . . . . . the only numerator factor that can be zero
e^(-1.3x) = 1/3 . . . . . . . . . add 3e^(-1.3x), divide by 3
-1.3x = ln(1/3) = -ln(3) . . take the logarithm
x = ln(3)/1.3 ≈ 0.845086 . . . . . . . divide by the coefficient of x
The function f(x) is decreasing for all values of x larger than this.
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Answer:
1. Total spent on transportation $222.2.
2. $ 192.5
3. She spends $30 over the guideline.
Step-by-step explanation:
As per the image attached:
Total monthly spent on transportation = Total monthly car payment + Spent on gas fuel
Total monthly spent on transportation = 120 + 37.9 + 28.4 + 35.9 = $222.2
So, Answer 1. Abby's total spent on transportation = $222.2
Calculating the percentage:
Calculating 11% as per the guideline:
Answer 2. As per the guideline, she should spend $192.5 on transportation.
Difference between spending and guideline = $222.2 - $192.5 = $29.7
Answer 3. She spends $29.7 over the guideline.