the growth of a bacteria each hour is given by the function f(x)= 5500(1.65)^x. At what percent are the bacteria growing each ho
1 answer:
The growth function per hour is
f(x) = 5500(1.65)ˣ
To find the growth rate per hour, we should find the derivative of f(x).
Take the natural log of the equation.
ln(f) = ln[5500(1.65)ˣ]
= ln(5500) + x ln(1.65)
Take the derivative with respect to x.
f'/f = ln(1.65) = 0.5
Therefore the derivative is
f' = 0.5f
= 2750(1.65)ˣ
= 275000(1.65)ˣ percent or 2.75 x 10⁵ (1.65)ˣ percent
Answer:
f(x) = 5500(1.65)ˣ
To find the growth rate per hour, we should find the derivative of f(x).
Take the natural log of the equation.
ln(f) = ln[5500(1.65)ˣ]
= ln(5500) + x ln(1.65)
Take the derivative with respect to x.
f'/f = ln(1.65) = 0.5
Therefore the derivative is
f' = 0.5f
= 2750(1.65)ˣ
= 275000(1.65)ˣ percent or 2.75 x 10⁵ (1.65)ˣ percent
Answer:
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Answer:
32
Step-by-step explanation:
We let the length of the square be l, the diagonal be z and the area be A.
Then by Pythagoras theorem;
The are of a square of length l is given as;
Combining these two equations yields;
Next, we have been given;
We are required to find;
when z = 4
By chain rule;
Differentiating with respect to z yields;
Therefore,
= 8z
When z is 4m the area of the square will be increasing at a rate of;
8m/min * 4m = 32