Question

type the correct answer in each box. use numerals instead of words. a scientist collects data on bacteria in a petri - dish. she finds that the number of bacteria grows exponentially and can be modeled using the equation (y = 16cdot1.8^{x}), where (x) is the number of hours after she sets up the experiment and (y) is the number of bacteria in the dish. complete the sentences to describe the model. the scientist started with around bacteria in the petri dish. each hour the number of bacteria increases by about %

Explanation:

Step1: Find the initial number of bacteria

When $x = 0$ (at the start of the experiment), we substitute $x=0$ into the equation $y = 16\times1.8^{x}$. Since any non - zero number to the power of 0 is 1, $y=16\times1.8^{0}=16\times1 = 16$.

Step2: Find the growth rate

The general form of an exponential growth equation is $y = a(1 + r)^{x}$, where $a$ is the initial amount and $r$ is the growth rate. Our equation is $y = 16\times1.8^{x}$, which can be written as $y=16\times(1 + r)^{x}$. So, $1 + r=1.8$, then $r=1.8 - 1=0.8$. To convert $r$ to a percentage, we multiply by 100, getting $r = 80\%$.

Answer:

16
80