i need help with this math homework problem

Question

A bacterial culture quadruples in size every hour. You begin observing the number of bacteria 3 hours after the culture is prepared. The amount (y) of bacteria (x) hours after the culture is prepared is represented by y=192(4^x-3). When will there be 200,000 bacteria? Round your answer to the nearest hundredth.

Answer 1

200000= 192(4^(x-3))

4^(x-3) = 200,000/192 =50,000/48=3125/3=1041 2/3

4^5=1024 x=8 hours

4^5.012=1041.2, x= 8.012 hours

x= about 8.01 hours to reach 200,000