The leaf litter decomposition function of gmelina arboreal at time (t) weeks is given by : y=250e^-t/3. Draw a graph showing the natural decay curve over the first 6 weeks. From the graph, find the nutrient loss after 3-4 weeks(3 weeks and 4 days)
geez - this has been done for you twice already.
Give it a rest, willya?
enter your equation here:
www.desmos.com/calculator
(copy and paste that as your URL, the program understands e
and use ^ to get into exponent mode)
You can set the domain and range by clicking on the tools button in the top right. I set my mine at 0 ≤ y ≤ 250, and 0 ≤ x ≤ 6
t = 3+4/7 = 3.57..
so your exponent = -(3 + 4/7)/3 or -1.1904
f(-1.1904) = 250e^-1.1904 = appr 76
If you slide your cursor along the curve, the point will be displayed
try to get x = 3.57 to get 76.055
yup
and I went through all that effort to do it again,
this is what happens when students become impatient.
To draw the graph of the leaf litter decomposition function for gmelina arboreal, we can use the given equation: y = 250e^(-t/3), where t represents the number of weeks.
To plot the graph, we need to evaluate the value of y (nutrient loss) at different weeks. To find the nutrient loss after 3-4 weeks (3 weeks and 4 days), we can substitute t = 3.571 weeks into the equation.
Let's proceed step by step:
Step 1: Calculate the values of y for each week in the first 6 weeks.
- For t = 0 weeks: y = 250e^(-0/3) = 250e^0 = 250
- For t = 1 week: y = 250e^(-1/3) ≈ 187.17
- For t = 2 weeks: y = 250e^(-2/3) ≈ 139.47
- For t = 3 weeks: y = 250e^(-3/3) = 250e^(-1) ≈ 92.86
- For t = 4 weeks: y = 250e^(-4/3) ≈ 69.34
- For t = 5 weeks: y = 250e^(-5/3) ≈ 51.67
- For t = 6 weeks: y = 250e^(-6/3) ≈ 38.47
Step 2: Plot the points obtained from the calculations above on a graph, with the x-axis representing the weeks (t) and the y-axis representing the nutrient loss (y).
Step 3: Connect the points with a smooth curve, representing the natural decay of nutrient loss over time.
Now, let's find the nutrient loss after 3-4 weeks (3 weeks and 4 days). Since this is a fraction of a week, we can convert it to a decimal by dividing 4 days by 7 days (one week):
4 days ÷ 7 days/week ≈ 0.571 weeks
Now, substitute t = 3.571 weeks into the equation:
y = 250e^(-3.571/3)
Evaluate the expression to find the nutrient loss after 3-4 weeks.