Math Problems?

Question

Predict the population of bacteria for each situation and time period
1. 55 bacteria that double every hour?
a. After 3 hours
b. After 5 hours
2. 125 bacteria that double every hour?
a. After 6 hours
b. After 8 hours
3. 33 e. coli bacteria that double every 30 min?
a. After 1 Hour
b. after 6 hours
4. 75 e coli bacteria that double every 30 min?
a. After 2 hours
b. After 3 hours
5. 225 bacteria that triple every hour?
a. After 1 hour
b. After 3 hours
6. 775 bacteria that triple every hour
a. After 2 hours
b. After 4 hours

Answer 1

If period is P then after k such a periods
for doubling the population will be 2^k*x,
and for tripling 3^k*x, where x is the initial population.
Therefore:

1.a. 2^3*55 = 440
b.1760

2.a. 8000
b. 32000

3.a. 132
b. 135168

4.a. 1200
b. 4800

5.a. 3^1*225 = 675
b. 3^3*225 = 6075

6.a. 6975
b. 62775.

Answer 2

If they double every hour, set n = # of hours, then the solution is:
initial amount * 2^n

If they double every 30 minutes, the solution is:
initial amount * 4^n

If they triple every hour, the solution is:
initial amount * 3^n