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Bacteria colonies can triple in size every 4 days. If you start with 40 bacteria microorganisms, how large would the colony be after 20 days? First, complete the equation: Future Amount = 40(1 + [?])0

Bacteria Colonies Can Triple In Size Every 4 Days If You Start With 40 Bacteria Microorganisms How Large Would The Colony Be After 20 Days First Complete The Eq class=

Sagot :

Exponential Growth

Some real-life events grow in such a way that they can be modeled as an exponential function, given as:

[tex]C(t)=C_o(1+r)^t[/tex]

Where C(t) is the future value of the measured variable, Co is its initial value, r is the growth rate and t is the time.

We are given the following data:

Initial amount: Co=40 bacteria

Growth rate: 1 + r = 3

The bacteria triples every 4 days, thus t is the number of periods of 4 days.

Thus the model is:

[tex]C(t)=40(3)^t[/tex]

We can solve the equation

1 + r = 3

And get r = 2. Rewriting the equation:

[tex]C(t)=40(1+2)^t[/tex]

We are required to find the number of bacteria after 20 days, that is, after 20/4 = 5 periods of 4 days. Substituting:

[tex]C(5)=40(3)^5[/tex]

Calculating:

[tex]C(5)=40\cdot243=9,720[/tex]

The colony would have 9,720 bacteria after 20 days

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