a growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. what is the…

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?\no y = 1,000(1.15)^6; 2,313 bacteria\no y = 1,000(1.15)^7; 2,660 bacteria\no y = 1,000(1.5)^5; 7,594 bacteria\no y = 1,000(1.5)^6; 11,391 bacteria

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?\no y = 1,000(1.15)^6; 2,313 bacteria\no y = 1,000(1.15)^7; 2,660 bacteria\no y = 1,000(1.5)^5; 7,594 bacteria\no y = 1,000(1.5)^6; 11,391 bacteria

Answer

Explanation:

Step1: Identify the 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.

Step2: Determine the values of $a$, $r$, and $t$

Here, $a = 1000$, $r=0.15$ (since 15% = 0.15), and $t = 6$.

Step3: Substitute the values into the formula

$y=1000(1 + 0.15)^6=1000(1.15)^6$.

Step4: Calculate the value of $(1.15)^6$ and then multiply by 1000

$(1.15)^6\approx2.31306$, and $1000\times2.31306 = 2313.06\approx2313$.

Answer:

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