Question 10 [10 points] The number of frogs in a pond increases continuously at a rate proportional to the number present. There
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Answer:
The number of bacteria after will be
Step-by-step explanation:
Given the initially 30 bacteria present in the culture.
Also, the number of bacteria got doubled every hour.
So, using the equation
Where is number of bacteria after
hours.
is bacteria present initially.
is the common ration, in our problem it is given that bacteria doubles every hour. So,
And is the number of hours. In our problem we need amount of bacteria at the end of
hours. So,
Plugging values in the formula we get,
So, number of bacteria after will be
The vertex-form equation is
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}