Answered: At 12:00 noon, there were 225 bacteria…

At 12:00 noon, there were 225 bacteria present. By 4:00 pm, there were 427 bacteria. If the bacteria grows continuously, how many will there be at 7:30 pm?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 2ECP

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Question

At 12:00 noon, there were 225 bacteria present. By 4:00 pm, there were 427 bacteria. If the bacteria grows continuously, how many will there be at 7:30 pm?

Expert Solution

Step 1

Let us consider the equation of exponential growth is

$y = c \times a^{t}$

Where, $y =$ The amount at any time

$c =$ The initial amount $= 225$

$a =$ The growth factor

$t =$ Time

Now, at time $4 : 00 p m$ that is $t = 4$ , $y = 427$

Substitute the values and further simplify it

$\begin{array}{l} 427 = 225 \times a^{4} \\ \Rightarrow \frac{427}{225} = a^{4} \\ \Rightarrow a = {(\frac{427}{225})}^{\frac{1}{4}} \end{array}$

Hence, $a = {(\frac{427}{225})}^{\frac{1}{4}}$ .

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