Question

The number of bacteria in a lab experiment can be modeled by the function P(t)=47(1.112)^{5t}.P(t)=47(1.112)
5t
. Write an equivalent function of the form P(t)=ab^t.P(t)=ab
t
. Round your final values to 4 decimal places.

Answer 1

SOLUTION

GIVEN

The number of bacteria in a lab experiment can be modeled by the function

$\sf \: P(t) = 47 {(1.112)}^{5t}$

TO DETERMINE

The equivalent function of the form

$\sf \: P(t) = a. {b}^{t}$

Round the final values to 4 decimal places.

EVALUATION

Here it is given that the number of bacteria in a lab experiment can be modeled by the function

$\sf \: P(t) = 47 {(1.112)}^{5t}$

Which can be rewritten as below

We use the formula

$\boxed{ \: \: \sf \: {( {a}^{m} )}^{n} = {a}^{mn} \: \: }$

Thus we have

$\sf \: P(t) = 47 {(1.112)}^{5t}$

$\sf \implies P(t) = 47 \times {({(1.112)}^{5}) }^{t}$

$\sf \implies P(t) = 47 \times {(1.70029) }^{t}$

Rounding off to 4 decimal places we get

$\sf P(t) = 47 \times {(1.7003) }^{t}$

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Answer 2

Answer:

P(t)=47(1.7003)^t

Step-by-step explanation:

Have a good day :)