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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?

Verified Answer :

54,273 = A * 1.70^6       where A  is the initial number
 A = 54273/1.70^6 =   2248

Answer: The initial number of fungi in the culture is 2248.

Step-by-step explanation:

Since we have given that

Rate of growth for a certain type of fungi = 70% per hour

Number of hours = 6

Number of fungi = 54,273

So,we  will apply the exponential function :

\(A=A_0(1+r)^t\)

Here, A = 54,273

r = 70% = 0.7

t = 6

So, our equation becomes,

\(54,273=A_0(1+0.7)^6\\\\54,273=A_0(1.7)^6\\\\\dfrac{54273}{1.7^6}=A_0\\\\A_0=2248.48\approx 2248\)

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

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