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?

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 , 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.

So the exponential function 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 and in our growth function.

Upon dividing both sides of our equation by 24.137569 we will get,

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

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0