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

The amount of bacteria each hour is 63.84 and

The amount of bacteria after 8 hours is 141.12

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+(rate)/(100))^(time)`

Or, The number of bacteria after 1 hours = i ×
`(1+(r)/(100))^(t)`

Or, f = 57 ×
`(1+(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+(rate)/(100))^(time)`

Or, The number of bacteria after 8 hours = i ×
`(1+(r)/(100))^(t)`

Or, n = 57 ×
`(1+(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