Question

The relative growth rate for a certain type of fungi is 60% per hour.A small culture has formed and in just 6 hours the count shows to be 20,273 fungi in the culture.What is the initial number of fungi in the culture?

Answer 1

Answer:

1208 =a

Step-by-step explanation:

The equation for growth is

y= ab^x

where a is the initial value and

b= 1+growth rate

b= 1+.60

b= 1.6

We know that in 6 hours   (x=6)   there are 20274 fungi  (y= 20273)

Substitute into the equation

20273 = a (1.6)^6

Divide by  (1.6)^6 on each side

20273 / (1.6)^6 =  a (1.6)^6/ 1.6^6

20273 / (1.6)^6 =  a

1208.36 = a

Rounding to a whole number

a = 1208

Answer 2

Answer: 1208.365

Step-by-step explanation:

Let P be the initial number of the fungi in the culture,

Since, The relative growth rate for a certain type of fungi is 60% per hour,

⇒ The number of fungi is increasing by the constant rate of 60%

⇒  $\text{ The number of fungi after 6 hours} =P(1+\frac{60}{100})^6$

According to the question,

$P(1+\frac{60}{100})^6=20,273$

$P\times 16.777216=20,273$

$P = 1208.365$