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

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.