Malte is collecting empty beer cans. He has got 1000 different cans and the number of cans seems to increase?

Question

by 5% each year. He has room for 2500 cans in his house. How many years will it take before Malte has to move out?

the answer is 18.8 years , how?

Answer 1

use this formula:
I = P (1 + r)^t

I = final amount (2500)
P = intial amont (1000)
r = rate (5% or .05)
t = time in years

so plug in chunks
2500 = 1000(1 + .05)^t
2.5 = (1.05)^t
log2.5 = t (log1.05)
t = log2.5 / log1.05
t =~ 18.8 years


hope it helps!

Answer 2

Year 0 = 1000
Year 1 = 1000 + (1000 * .05) = 1050
Year 2 = 1050 + (1050 * .05) = 1102.5
...

We can also write this as

Year 0 = 1000
Year 1 = 1000 * 1.05
Year 2 = (1000 * 1.05) * 1.05

So Year n = 1000 * 1.05^n

So we need to solve 2500 = 1000 * 1.05^n

Classic method is the use of log's

log(2500) = log (1000 * 1.05^n)
log(2500) = log (1000) + n log(1.05)
log(2500) - log(1000) = n log(1.05)
log(2500/1000)/log(1.05) = n
n = log(2.5)/log(1.05)

n = 18.780234653283442331531338963567

Answer 3

2500 = 1000(1.05)^y
2.5 = 1.05^y
ln(2.5) = yln(1.05)
y = ln(2.5)/ln1.05) = 18.78 years

Answer 4

the guy above explained it perfectly