Question

a culture started with 6,000 bacteria. After 4 hours, it grew to 6,600 bacteria. Predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number.

Answer 1

P = 6,600

A = 6,000

t = 4

k = ?

6600 = 6000e^(4k)

6600/6000 = e^(4k)

1.1 = e^(4k)

Take the natural log of both sides.

ln 1.1 = 4k ln e (remember that ln e = 1)

ln 1.1 = 4k

(ln 1.1) / 4 = k

k = 0.0238

Bacteria after 10 hours.

P = 6000e^(0.0238*10)

= 6000e^0.238

= 7612

Therefore, the bacteria will grow to 7612 after 10 hours.