MATH HELP PLEASEEEEE?
A population of bacteria is growing according to the function below, where t is time in hours.
B(t)=10,000 x e^0.17t
to the nearest hour how long will it take for the population to grow to 1,000,000?
PLEASE HELP ME
A population of bacteria is growing according to the function below, where t is time in hours.
B(t)=10,000 x e^0.17t
to the nearest hour how long will it take for the population to grow to 1,000,000?
PLEASE HELP ME
Anonymous
Favorite Answer
When the population reaches 1,000,000, B(t) = 1,000,000:
1,000,000 = 10,000 * e^0.17t
We must now make t the subject.
Divide both sides by 10,000:
e^0.17t = 1,000,000 / 10,000
e^0.17t = 100
Take natural log of both sides:
ln(e^0.17t) = ln(100)
0.17t = ln(100)
Divide both sides by 0.17:
t = ln(100) / 0.17
t = 27.089 hours
t = 27 hours (to the nearest hour)
Hope this helps.