Bacteria culture double in size?

Question

if a bacteria culture starts with 8000 bacteria and doubles in size every 30 minutes, how many minutes will it take for the population to reach 49000?

Answer 1

Recall the formula

Where

y = ending amount

b = growth or decay factor

a = initial amount

x = time

Write the equation

8000(2 )^t = 49000

(2 )^t = 49000/8000

(2 )^t = 49/8

Apply log on each side.

log (2 )^t =  log (49/8)

t log (2) = log(49/8)

t log(2) = log(6.125)

t = log(6.125)/log(2)

t = 2.614

2.614 * 30 = 78.42

78.42 minutes will take for the population to reach 49000.