A tangent is a line that touches a circle only at one point
5 x 3²⁴ bacteria will there be after one day.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Consider what is actually happening in the question.
You begin with 5 bacteria, and after 1 hour it has tripled so you now have
5x 3=15.
Next hour, it triples again so you now have 5 x 3 x 3=45
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴ means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
n x 324 where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is 5 x 3²⁴.
Hence 5 x 3²⁴ bacteria will there be after one day.
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We can turn this word problem into the following equation:
x^2 + 85 = (x - 17)^2
x^2 + 85 = x^2 - 34x + 289
-85 -85
_______________________
x^2 = x^2 - 34x + 204
+34x +34x
_______________________
x^2 + 34x = x^2 + 204
-x^2 -x^2
____________________
34x = 204
Divide 34 on both sides
x = 6.
The number is 6.
