africansoccer88
contestada

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?

Respuesta :

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

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 Β will apply the exponential function :

[tex]A=A_0(1+r)^t[/tex]

Here, A = 54,273

r = 70% = 0.7

t = 6

So, our equation becomes,

[tex]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[/tex]

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