We are given with
relative growth rate = 70%
time = 6 hours
count after 6 hours = 54273
And we are asked to fine the initial number of fungi. We use the equation:
54273 = Ao (1.7)^6
Solving for Ao
Ao = 2248
The initial number of fungi is 2248.
The initial number of fungi in the culture is 2248.
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
[tex]y = a(1-r)^{t}[/tex]
Where,
a is the initial value
r is the growth rate
t is the time
y is the final value
According to the given question.
Relative growth rate, r = 70% = [tex]\frac{70}{100} =0.7[/tex]
Time, t = 6hours
Final number of fungi after 6 hours, P = 54,273
Let the initial number of fungi in the culture be [tex]P_{o}[/tex].
Now, the exponential growth rate formula we can say that
[tex]P = P_{o}(1+r)^{t}[/tex]
Substitute the value of t = 6, r = 0.7 and P = 54,273 in the above question.
[tex]54,273 = P_{o} (1+0.7)^{6}[/tex]
⇒ [tex]54,273 = P_{o} (1.7)^{6}[/tex]
⇒ [tex]54,273 = P_{o} (24.14)[/tex]
⇒ [tex]P_{o} =\frac{54,273}{24.14}[/tex]
⇒ [tex]P_{o} = 2248[/tex]
Hence, the initial number of fungi in the culture is 2248.
Find out more information about exponential growth here:
https://brainly.com/question/1596693
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