The accompanying table shows the number of bacteria present in a certain culture over a 4 hour period, where x is the time, in h
ours, and y is the number of bacteria.Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the number of bacteria present after 16 hours, to the nearest whole number.
1 answer:
Answer:
Step-by-step explanation:
I really hope you know how to use your calculator to find regression equations, because in this forum it is impossible to teach you how to do that. I ran the data through my calculator and got the exponential equation as
which means at 4 hours, we started with 1963 bacteria and it is growing at a rate of 114% each hour. Since we started out with an x value of 0, and that value represents the number of bacteria after 4 hours, then time 0 is 4 hours, which means that time 12 is 16 hours. We replace the x in the equation with a 12 and do the math:
which gives us, in the end,
y = 9460
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Answer:
D = L/k
Step-by-step explanation:
Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is
dA/dt = in flow - out flow
Since litter falls at a constant rate of L grams per square meter per year, in flow = L
Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow
So,
dA/dt = in flow - out flow
dA/dt = L - Ak
Separating the variables, we have
dA/(L - Ak) = dt
Integrating, we have
∫-kdA/-k(L - Ak) = ∫dt
1/k∫-kdA/(L - Ak) = ∫dt
1/k㏑(L - Ak) = t + C
㏑(L - Ak) = kt + kC
㏑(L - Ak) = kt + C' (C' = kC)
taking exponents of both sides, we have
When t = 0, A(0) = 0 (since the forest floor is initially clear)
So, D = R - A =
when t = 0(at initial time), the initial value of D =
Answer:
$119
Step-by-step explanation:
Let
x -----> the number of skaters
y -----> the cost for birthday parties
we have the points
(10,107) and (15,137)
step 1
Find the slope of the linear equation
The formula to calculate the slope between two points is equal to
substitute the values
step 2
Find the equation of the line in point slope form
we have
substitute
step 3
Convert to slope intercept form
step 4
How much would a party for 12 skaters cost?
For x=12 skaters
substitute the value of x in the equation and solve for y
Answer:
Alfred ate 24 hot dogs.
Step-by-step explanation:
Let the number of hot dog ate by Olafs be represented by b.
Since Olafs eats five fewer than triple the hot dogs Alfred eats, and Alfred ate a hot dogs. This can be expressed in a mathematical equation as follows;
b = 3a - 5
But Olafs eats 67 hot dogs, so that b = 67. Thus;
b = 3a - 5
67 = 3a - 5
67 + 5 = 3a
3a = 72
divide both sides by 3 to have;
a =
a = 24
Alfred ate 24 hot dogs.