Question

zacks biology lab group is studying how quickly bacteria grow when exposed to sunlight. at the beginning of the experiment, zack looked at the sample under a microscope and counted 5 bacteria. after the sample was exposed to sunlight for one hour, zack looked again and counted 35 bacteria. write an exponential equation in the form y = a(b)^x that can model the number of bacteria, y, after x hours in sunlight. use whole numbers, decimals, or simplified fractions for the values of a and b. y =

Explanation:

Step1: Determine the value of a

The initial number of bacteria is $a$. At the start ($x = 0$), $y=5$, so $a = 5$.

Step2: Determine the value of b

We know that when $x = 1$, $y = 35$ and $a = 5$. Substitute into $y=a(b)^x$: $35=5(b)^1$. Solve for $b$ by dividing both sides by 5. $\frac{35}{5}=b$, so $b = 7$.

Answer:

$y = 5(7)^x$