Question

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

Answer 1

Answer:

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

Step-by-step 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 $b=1+15\%=1+\frac{15}{100}=1+0.15=1.15$

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:

$15\% of 1800 =0.15\times 1800=270$

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.