The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)
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; https://brainly.com/question/27161222
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