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

Explanation:

Step1: Identify growth formula

The exponential growth formula is $y = a(1+r)^t$, where $a$ = initial amount, $r$ = daily growth rate, $t$ = time in days.

Step2: Plug in given values

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

Step3: Calculate the value

First compute $1.15^6 \approx 2.31306$, then multiply by 1000: $1000 \times 2.31306 = 2313.06$

Answer:

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