Question

To begin a bacteria study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 15%.

Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.

Answer 1

The exponential function is
`C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1`

Explanation:

Given

`t` be the number of hours.

`y` number of bacteria cells.

And we know that an exponential function is
`C(t)=y(b)^t`,where
`b` is a positive real number, and in which the argument
`t` occurs as an exponent

The petri dish has
`1800` bacteria cells we can say that
`y=1800`

In the equation as
`C` is function of time and
`(t)` will vary as
`1,2,3` for respective hours.

To find the value of
`b` we have to understand that it is dependent on percent increase if there is increment of
`15\%` then
`b=1+15\%=1+(15)/(100)=1+0.15=1.15`

So the exponential function will be
`C(t)=y(b)^t` ,plugging the values it will be equivalent to
`C(t)=1800(1+0.15)^1`

Check:

`15\% of 1800 =0.15* 1800=270`

So in first hour the cells will increased by a quantity of
`270` cells.

The number of cells after an hour in the petri dish
`=(1800+270)=2070`

That can also be from the formula.

`C(t)=1800(1.15)^1=2070`

So the exponential function is
`C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1`

`y` will increase exponentially as the value of
`t` increase.