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The relative growth rate for a certain type of fungi is 70% per hour. a small culture has formed and in just 6 hours the count shows to be 54,273 fungi in the culture. what is the initial number of fungi in the culture?

User Lvollmer
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1 Answer

4 votes

Answer:

2248.

Explanation:

We have been given that the relative growth rate for a certain type of fungi is 70% per hour. This means that fungi is growing exponentially.

Since we know that an exponential function is in form
y=a*b^x, where,

a = Initial value.

b = For growth b is in form (1+r), where r represents rate in decimal form.

Let us convert our given rate in decimal form.


70\%=(70)/(100)=0.70

So the exponential function
y=a*(1.70)^x represents the growth of fungi after x hours.

We are also told that in just 6 hours the count shows to be 54,273 fungi in the culture.

To find the initial number of fungi in the culture we will substitute
y=54,273 and
x=6 in our growth function.


54,273=a*(1.70)^6


54,273=a*24.137569

Upon dividing both sides of our equation by 24.137569 we will get,


(54,273)/(24.137569)=(a*24.137569)/(24.137569)


2248.48658=a


a\approx 2248

Therefore, the initial number of fungi in the culture is 2248.

User Salman Kazmi
by
8.2k points
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