Answer:
2248.
Step-by-step 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.
\(70\%=\frac{70}{100}=0.70\)
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,
\(\frac{54,273}{24.137569}=\frac{a*24.137569}{24.137569}\)
\(2248.48658=a\)
\(a\approx 2248\)
Therefore, the initial number of fungi in the culture is 2248.