Answer:
Step-by-step explanation:
It often works well to write an exponential expression as ...
value = (initial value)×(growth factor)^(t/(growth period))
(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...
P(t) = 100·2.3^t
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(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours
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(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t
P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour
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(d) We want to find t such that ...
P(t) = 10000
100·2.3^t = 10000 . . . substitute for P(t)
2.3^t = 100 . . . . . . . . divide by 100
t·log(2.3) = log(100)
t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000
The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.
The sides of the triangle are given as a = 20, b = 15, and c = 25.
We will use Hero's formula to find the area of this triangle.
<h3>What is Heron's formula?</h3>It is a three-face polygon that consists of three edges and three vertices.
We use Heron's formula to find the area of a triangle with 3 sides:
Herons formula:
Area of a triangle =
Where a, b, and c are sides of a triangle.
And s = semi perimeter of a triangle.
s =
If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.
Let the given sides be:
a = 20, b = 15 and c = 25.
(20 + 15) > 25
(20 + 25) > 15
(15 + 25) > 20 so the given sides are true.
Now,
Semi perimeter of the triangle:
s = (a+b+c) / 2
s = (20+15+25) / 2
s = 60 / 2
s = 30
Putting s = 30 in the area of the triangle.
we get,
Area of the triangle =
Area of the triangle =
Thus, the area of a triangle is 150.
Learn more about the Area of triangles here:
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