The prime factorizations of 16 and 24 are shown below.
2 answers:
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Answer: There were 1,250 bacteria present initially.
Step-by-step explanation:
To find the exponential growth to this, lets create an exponential model shown as below:
f(x) = a()
Let y represent the amount of hours have passed after the third-hour recording. With the information given, we can create a set of input-output pairs: (0 , 10000) and (2 , 40000). Now that we have this set of pairs, we have given ourselves the initial value of the function, a = 10,000. We can now substitute the second point into the equation using N = 40,000.
N(y) = 10000b^y
40000 = 10000b^2 Divide and write in lowest terms.
÷10000 ÷10000
4 = b^2
b = Isolate b using properties of exponents.
b = 2
Now that we have the exponential growth, we can use b = 2 to work backwards and find the initial amount of bacteria.
10,000 ÷ 2 = 5,000 <-- Amount of bacteria 2nd hour
5,000 ÷ 2 = 2,500 <-- Amount of bacteria 1st hour
2,500 ÷ 2 = 1,250 <-- Initial amount of bacteria.
The initial amount of bacteria is 1,250
Answer:
The tree is 16.25 m tall.
Step-by-step explanation:
Attached is a diagram that better explains the problem.
From the diagram we see that the distance between the top of the tree and the line of sight of the observer is x.
To find the height of the tree, we need to first find x and then add it to the height of the observers line of sight from the ground.
Using SOHCAHTOA trigonometric function:
tan(20) = x/39.2
=> x = 39.2 * tan(20)
x = 39.2 * 0.364
x = 14.27m
Hence, the height of the tree is:
(14.27 + 1.98)m
16.25m
The tree is 16.25 m tall.
