Answer: (a, 0)
<u>Step-by-step explanation:</u>
Notice that S is on the x-axis, therefore the y-coordinate is "0".
Notice that S has the same x-value of R. The x-value of R is "a".
An applicable equation of a vertical parabola in vertex form is:
y-k = a(x-h)^2
Let x=2, y=4, h=-1 and k=-1, where (h,k) is the vertex. Then,
4-(-1) = a(2-[-1])^2, which becomes 5 = a(9). Therefore, a = 5/9, and the
equation of the parabola is
y+1 = (5/9)(x+1)
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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