The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)
<h3>How to calculate Exponential Growth?</h3>
The formula for exponential growth is;
P = P₀e^(rt)
where;
P = current population at time t
P₀ = starting population
r = rate of exponential growth/decay
t = time after start
Thus, from our question we have;
4500 = 1500 * e^(r * 1)
4500/1500 = e^r
e^r = 3
In 3 = r
r = 1.0986
Thus, the function that represents the growth of this culture of bacteria as a function of time is;
P = 1500e^(1.0986t)
For the culture to double, then;
P/P₀ = 2. Thus;
e^(1.0986t) = 2
In 2 = 1.0986t
t = 0.6931/1.0986
t = 0.631 hours
Read more about Exponential Growth at; brainly.com/question/27161222
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Answer:
(x+16)²+(y-30)²=1156
Step-by-step explanation:
We have given:
center at (-16,30). It means h = -16 and k=30
and it passes through the origin (0,0)
Thus the radius will be distance between (-16,30) and (0,0)
r=√(-16 - 0)²+(30-0)²
r=√256+900
r²=(√1156)²
r²=1156
Now apply standard equation of circle:
(x-h)²+(y-k)² = r²
(x+16)²+(y-30)²=1156
Thus the equation is (x+16)²+(y-30)²=1156 ....
Answer:
Amira used 4 balloons for each balloon animal.
Step-by-step explanation:
From the table, we can conclude that:
For 20 animals being sold by her, the leftover balloons were 180.
Then there is an increase in the number of animals being sold. She now sells 29 animals. So, the increase in animals being sold is given as:
29 - 20 = 9.
So, 9 more animals were sold. The balloons used for these 9 animals can be obtained by taking the difference of the leftover balloons for the two days.
The difference of the leftover balloons = 180 - 144 = 36.
So, 36 balloons were used for selling 9 more animals.
Similarly, there is an increase of another 9 animals when 38 animals were sold as 38 - 29 = 9. Also, the balloons used in this case is 36 only as the difference of the leftover balloons is 36.
144 - 108 = 36
Therefore, we conclude that for selling 9 balloon animals, Amira used 36 balloons.
Number of balloons used for 9 balloon animals = 36
∴ Number of balloons used for 1 balloon animal = 
(Unitary method)
Thus, Amira used 4 balloons for each balloon animal.
Answer:
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
I just did it off of A.P.E.X
That's simple!!!
-12/19 = b/19
as denominators are same, you can cancel that.
b = -12
