Question

To begin a bacteria study a petri dish had 2200 bacteria cells every hours since the number of cells has increased by 3.8% let t be the number of hours since the start of the study let y be the number of bacterial cells write the exponent to function showing the relationship between y&t

Answer 1

Therefore the required relationship is

`y = 2000(1.038)^t`

Explanation:

Given that, to begin a bacteria study a petri dish had 2200 bacteria cells every hours.

The growth of bacteria is in exponential.So we use the following formula

`A=P(1+r)^n`

A= Total amount =y = the number of bacteria cell

P= initial value = 2000

r= rate of increase = 3.8%= 0.038

n = time = t

Putting the all values

`y=2000(1+0.038)^t`

`\Rightarrow y = 2000(1.038)^t`

Therefore the required relationship is

`y = 2000(1.038)^t`