Acertain bacteria population is known to quadruples every 150 minutes. suppose that there are initially 200 bacteria.
what is the size of the population after t hours?

This is a geometric progression
The size of the population afeter t hours will be=a₁*r^n

a₁= the first term =200
r=common ratio=4

150 minutes=150 minutes * (1 hour /60 minutes)=2.5 hours.

In this case:
the size of the populatation after t hours=200*4^t/2.5=200*4^0.4t

To check
 t=0⇒ the size will be=200*4⁰=200*1=200
t=2.5 hours=150 minutes; the size will be =200*4¹=800
t=5 hours; the size will be=200*4²=200*16=3200

the size will be= 200*4^(0.4t)

Number 5 is 50 degreesnumber 6 is 45 degreesnumber 7 is 60 degreesnumber 8 is 45 degrees