After t hours there are P(t) cells present in a culture, where P(t)equals2000e Superscript 0.3 t. (a) How many cells were present initially? (b) Give a differential equation satisfied by P(t). (c) When will the population double? (d) When will 8 comma 000 cells be present?

(a)2000 of cells were present initially.

(b)The differential equation of the given exponential model is

(c)The population will be double after 2.31 hours.

(d)The number of cell will be 8,000 after 4.62 hours.

Step-by-step explanation:

Given that,

where P(t) is number of cell and t is time in hours.

(a)

Initial time means t=0.

Putting t=0 i the given expression

2000 of cells were present initially.

(b)

The differential equation of population growth is

The solution of the above equation is

Comparing the given exponential model to the above solution

So, k= 0.3 and C=2000

The differential equation of the given exponential model is

(c)

If the population double then P(t) = 2× P(0) =2×2000

Taking ln both sides

h

The population will be double after 2.31 hours.

(d)

Now P(t)=8,000

Taking ln function both sides

h

The number of cell will be 8,000 after 4.62 hours.

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step-by-step explanation:

step-by-step explanation: