How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 85%

So you are seeing how much time it'll take so you solve for "t", the time.

So you take the formula A=Pe^ (rt)

A=2000 because it's the end value

P=20 because it's the starting value

r=.85 since 85%=.85 and. 85 is the rate

Plug the values in and you get 2000=20e^ (.85t)

What you do is you divide by 20 so you get 100=e^ (.85t)

Take the natural logarithm of both sides 'cause of e and a natural log is written as ln so you get

ln 100=.85t ln e and because you can use the power rule you end up with. 85t ln e and

ln e=1 so you have ln 100 =.85t so you divide by. 85 so (ln 100) /.85=t and t=5.4178472776331

hours

3. Exponential decay:

A = Pe^ (rt)

where

A is the final amount

P is the initial value

r is rate of decay

t is time (years)

Let's say x is the initial amount then (1/2) x=xe^ (32r)

I used x because the value isn't given but anyway division by x would give you 1/2=e^ (32r)

Take the ln of both sides so ln 1/2=32r ln e and then ln e=1 so ln 1/2=32r.

Divide both sides by 32 and you'd get (ln 1/2) / 32=r and r = - 0.021660849392498

4. Another depreciation question.

Each year the item retains 88% of its last-year value.

Solve: 250,000 (0.88) ^x = 100,000

0.88^x = 0.4

x = [log0.4]/[log0.88]

x = 7.168 years