Question

Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours, and Jaquan starts with 80 bacteria that double every 3 hours. x= number of DAYS. Would Colby's experiment be modeled by... y=50(2)^x y=50(2)^8x or y=50(2)^12x Would Jaquan's experiment be modeled by... y=80(2)^x y=80(2)^8x or y=80(2)^12x

Answer 1

Given that x=number of days
To model the expressions we use the exponential growth given by:
y=a(b)^nx
where:
a=initial value
b=growth factor
n=24 hours
thus Colby's experiment will be:
y=50(2)^(1/2*24*x)
y=50(2)^(12x)
N/B we multiply by 24 so as to convert days into hours

b] Jaquan's starts with 80 bacteria that double every 3 hours.
a=80, b=2
thus
y=80(2)^(1/3×24×x)
simplifying the above we get:
y=80(2)^(8x)