Ascientist is growing bacteria in a lab for study one particular type of bacteria grows at a rate of y=2t^2+3t+500 a different bacteria grows at a rate of y=3t^2+t+300 in both of these eqiations y is the number of bacteria after t minutes when is there an equal number of both types of bacteria

ANSWER

t=15 minutes.

EXPLANATION

The equation that models the growth rate of the first type of bacteria is,



The growth rate of a second type of bacteria is modeled by:



Since y is the number of bacteria after t minutes in both equations, we equate both equations to find the time when there is an equal number of both types of bacteria.



We rewrite as standard quadratic equation,





We use the quadratic formula to obtain,









t=-13.177 or t=15.177

We discard the negative value. Hence there is an equal number of both types of bacteria after approximately 15 minutes.