Question

a growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. what is the population of the culture 6 days after inoculation?
o y = 1,000(1.15)^6; 2,313 bacteria
o y = 1,000(1.15)^7; 2,660 bacteria
o y = 1,000(1.5)^5; 7,594 bacteria
o y = 1,000(1.5)^6; 11,391 bacteria

Explanation:

Step1: Identify the exponential - growth formula

The formula for exponential growth is $y = a(1 + r)^t$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time. Here, $a = 1000$, $r=0.15$, and $t = 6$.

Step2: Substitute the values into the formula

Substitute $a = 1000$, $r = 0.15$, and $t = 6$ into $y=a(1 + r)^t$. We get $y=1000(1 + 0.15)^6=1000(1.15)^6$.

Step3: Calculate the value of $(1.15)^6$

$(1.15)^6=1.15\times1.15\times1.15\times1.15\times1.15\times1.15\approx2.313$.

Step4: Calculate the value of $y$

$y = 1000\times2.313 = 2313$.

Answer:

A. $y = 1,000(1.15)^6; 2,313$ bacteria