Question

SIXTY POINT OFFER.

James is studying newly discovered bacteria in a petri dish. At time t = 0 there is 57 bacteria found in the dish. This bacteria is growing at a 12% rate every hour.

A. Write the function f(x) that represents the amount of bacteria found each hour.

B. Explain what x represents.

C. Explain what f(x) represents.

D. If it continues at this rate, how much bacteria will be in the dish after 8 hours.

Answer 1

Answer:

The amount of bacteria each hour is 63.84 and

The amount of bacteria after 8 hours is 141.12

Step-by-step explanation:

Given as :

The initial number of bacteria = i = 57

The rate of grow of bacteria = r = 12%

The number of bacteria after 1 hours = f

Let The number of bacteria after 8 hours = n

Now, According to question

The number of bacteria after n hours =  initial number of bacteria × $(1+\frac{rate}{100})^{time}$

Or, The number of bacteria after 1 hours = i  × $(1+\frac{r}{100})^{t}$

Or, f =  57 × $(1+\frac{12}{100})^{1}$

Or, f =  57 × $(1.12)^{1}$

Or, f =  57 × 1.12

Or, f =  63.84

So,The number of bacteria after 1 hour  = f = 63.84

Hence, The number of bacteria after 1 hours is 63.84  Answer

Again

The number of bacteria after n hours =  initial number of bacteria × $(1+\frac{rate}{100})^{time}$

Or, The number of bacteria after 8 hours = i  × $(1+\frac{r}{100})^{t}$

Or, n =  57 × $(1+\frac{12}{100})^{8}$

Or, n =  57 × $(1.12)^{8}$

Or, n =  57 × 2.4759

Or, n =  141.12

So,The number of bacteria after 8 hours = n = 141.12

Hence, The number of bacteria after 8 hours is 141.12  Answer