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?
○ y = 1,000(1.15)^6; 2,313 bacteria
○ y = 1,000(1.15)^7; 2,660 bacteria
○ y = 1,000(1.5)^5; 7,594 bacteria
○ y = 1,000(1.5)^6; 11,391 bacteria

Explanation:

Step1: Identify the 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 number of time - periods. Here, $a = 1000$, $r=0.15$, and $t = 6$.

Step2: Substitute the values

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

Step3: Calculate the value

Calculate $(1.15)^6\approx2.313060766$. Then $y = 1000\times2.313060766\approx2313$ bacteria.

Answer:

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