A bacterial culture quadruples in size every hour. You start to observe

Question

the number of bacteria 3 hours after the culture is prepared. The
amount of “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?
Use your calculator and include the steps you took to find your
answer. Round your answer to the nearest whole hour.

Answer 1

To find out when there will be 200,000 bacteria, we need to solve for x in the equation 𝑦 = 192(4^x-3) when y is equal to 200,000.

So, we set up the equation:
200,000 = 192(4^x-3)

Divide both sides by 192:
200,000/192 = 4^x-3

1,041.6667 = 4^x-3

Add 3 to both sides:
1,041.6667 + 3 = 4^x

4^x = 1,044.6667

Take the logarithm on both sides to solve for x:
log(4^x) = log(1,044.6667)

x * log(4) = log(1,044.6667)

x = log(1,044.6667) / log(4)

x ≈ 4.63

Therefore, there will be 200,000 bacteria approximately 4.63 hours after the culture is prepared. Rounded to the nearest whole hour, there will be 200,000 bacteria after 5 hours.