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
