A bacteria triples its original population in 25 hours (A=3A0). How big will its population be in 100 hours?

81 times the original size.

Step-by-step explanation:

AA0ktA=3A0=?=?=25hours=A0ekt

Substitute the values in the formula.

3A0=A0ek⋅25

Solve for k. Divide each side by A0.

3A0A0=e25k

Take the natural log of each side.

ln3=lne25k

Use the power property.

ln3=25klne

Simplify.

ln3=25k

Divide each side by 25.

ln325=k

Approximate the answer.

k≈0.044

We use this rate of growth to predict the number of bacteria there will be in 100 hours.

AA0ktA=3A0=?=ln325=100hours=A0ekt

Substitute in the values.

A=A0eln325⋅100

Evaluate.

A=81A0

At this rate of growth, we can expect the population to be 81 times as large as the original population.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.