Question

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?

Answer 1

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.