Answer:
a)1280 bacteria
Step-by-step explanation:
We find the function in t hours first
Bacteria in a petri dish doubles every 10 minutes. (Express in exponential function)
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
The formula to use is given as
y = Ab^t
Where
y = Total Population of bacteria
B= initial population of the bacteria
r =
t = time in hours
The bacteria doubles in the petri dish every 10 minutes, we have 10 bacteria
10 minutes in hours = 10/60= 1/6 hours
10 × 2 = 10b^10/60
20 = 10b ^1/6
2 = b^1/6
Multiply both sides by Power of 6
2^6 = b
b = 64
Hence, y = 10×(64)^t
a) If there are 10 bacteria initially, how many are there after 120 minutes?
120 minutes in hours = 2
y = 10(64)²
y = 1280
There would be 1280 bacteria after 120 minutes
b) If there are 10 bacteria initially, when would there be a million bacteria?
y= 1,000,000
A = 10 bacteria
b = 64
t = ???
1000000 = 10 × (64)^t
Divide both sides by 10
100000 = (64)^t
Answer:
y = 4x² - 16x + 16
Step-by-step explanation:
Standard form is y = ax² + bx + c
To convert from vertex form to standard form multiply out the equation
1. Solve (x-2)² using F.O.I.L.
(x - 2) · (x - 2) = x² - 4x + 4
y = 4(x² - 4x + 4)
2. Distribute the 4
y = 4x² - 16x + 16
What are the options for this?
This problem Is an example of geometrica progression. The formula
for the sum of geometric progression is:
S = a[(r^n)-1] / (r – 1)
Where s is the sum
a is the first term = 1
r is the common ratio = 2 ( because it doubles every year
n is the number of terms = (19) since the first term is when
he was born which he still 0
s = S = 1[(2^19)-1] / (2 – 1)
s = $524,287
<span> </span>
Answer: A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.