geometric sequences

Question

A colony of bacteria is growing at a rate of 50% per hour.

If this rate of growth remains the same and the colony starts with 100 bacteria, approximately how many bacteria will there be after 6 hours?

Answer 1

100

1 hour 150

2 hours 225

3 hours 337.5

4 hours 506.25

5 hours 759.375

6 hours 1,139.0625

It's a geometric sequence with common ratio r=1.5

an=ao(r^n)

an = 100r^n

an=100(1.5)^n

a6 = 100(1.5)^6 = 100(11.390625) = 1,139,0625

round off to nearest integer + 1,139 bacteria