# In a lab experiement, there is a culture that contains 25 bacteria at 2:00. At 2:15 there are 50...

## Question:

In a lab experiement, there is a culture that contains 25 bacteria at 2:00. At 2:15 there are 50 bacteria, At 3:15 there are 800 bacteria. What is the conjecture about the rate at which the bacteria increase?

## Exponential growth

Exponential growth is an exponential where the growth in the value is a part of the growing value. For example, If a base value is increasing at a certain rate, after each period of time, the original value will increase. The increased value will be taken as the new base value upon which the increment is calculated.

It can be formulated as:

$$Final\ value\ =\ Initial\ value\times (1 +\dfrac{rate}{100})^{Time}$$

## Answer and Explanation:

According to the question, The number of bacteria at 2:00 was 25 that increased to 50 at 2:15.

Using exponential growth fomula:

$$Final\ value\ =\ Initial\ value\times (1 +\dfrac{rate}{100})^{Time}$$

$$50=25(1+\dfrac{R}{100})^{15}$$

Dividing equation by 25

$$2=(1+\dfrac{R}{100})^{15}$$

Taking root of 15 on both sides

$$\sqrt[15]{2}=\sqrt[15]{(1+\dfrac{R}{100})^{15}}$$

$$1.0473=1+\dfrac{R}{100}$$

$$\dfrac{R}{100} =0.0473$$

Multiplying both sides by 100

$$R=4.73\%$$

The rate of bacterial growth is {eq}4.73\% {/eq} per minute