# Math Help - percentages

1. ## percentages

Hi, this question has two parts so i will tell you part 1 first:
A toy rabbit works using a single battery. When the battery is new, it has 250 units of power. After every hour of use the battery loses 20% of its remaining power.
How many units of power remain in the battery after 2 hours?
10% of 250= 25
25 x 4= 100
250 - 100= 150
150 units remaining

PART B

The battery must have at least 100 units of power left for the toy rabbit to work.
Show that the toy rabbit will still be working after 4 hours.

i don't understand because, 100untis if from 2 hours so 100 x 2=200 = 4 hours
250-200=50 but it needs at least 100units to work

2. Originally Posted by andyboy179
Hi, this question has two parts so i will tell you part 1 first:
A toy rabbit works using a single battery. When the battery is new, it has 250 units of power. After every hour of use the battery loses 20% of its remaining power.
How many units of power remain in the battery after 2 hours?
10% of 250= 25
25 x 4= 100 20% per hour is not 40% in 2 hours
250 - 100= 150
150 units remaining

PART B

The battery must have at least 100 units of power left for the toy rabbit to work.
Show that the toy rabbit will still be working after 4 hours.

do i do another 2 hours from the 150 units left? or is it 4 hours from a new battery, 250untis?
Hi andyboy179,

A loss of 20% in the first hour loses 20% of 250, which is 50,
leaving 200 units remaining after an hour.
A loss of 20% in the second hour loses 20% of the remaining 200 units.

Continue this process for the next 2 hours to answer the two questions.

3. Originally Posted by Archie Meade
Hi andyboy179,

A loss of 20% in the first hour loses 20% of 250, which is 50,
leaving 200 units remaining after an hour.
A loss of 20% in the second hour loses 20% of the remaining 200 units.

Continue this process for the next 2 hours to answer the question.

but it says 1 hour loses 20%, 20%= 50 but it wants 2 hours so 50+50=100
250-100=150

4. sorry i get it now!!! so 20% of 200= 20
50+20=70
250-70=180

now is where im stuck do i do 180-70=110 to get part be correct?

5. Originally Posted by andyboy179
sorry i get it now!!! so 20% of 200= 20
50+20=70
250-70=180

now is where im stuck do i do 180-70=110 to get part be correct?
Pretty good but 20% of 200 = 200/5 = 40

You can either take 40 from 200 or take (50+40) from 250. Both expressions equal 160 which is correct

6. Originally Posted by e^(i*pi)
Pretty good but 20% of 200 = 200/5 = 40

You can either take 40 from 200 or take (50+40) from 250. Both expressions equal 160 which is correct
thanks, but when i got 160 would i do 20% of that = 32
160-32=128
20%128= 25.6???

7. Originally Posted by andyboy179
thanks, but when i got 160 would i do 20% of that = 32
160-32=128
20%128= 25.6???
That's right.

There is a formula for this if you don't want to show all the steps:

$P_t = P_0 \cdot 0.8^t$

Where
• $P_t$ = power at time t
• $P_0$ = power at time 0 (250)
• $t$ = time
• $0.8 = 1-0.2$ where 0.2 is the 20% power loss

For example at time 0: $P_t = 250 \cdot 0.8^0 = 250$

At time 1: $P_t = 250 \cdot 0.8^1 = 200$
At time 2: $P_t = 250 \cdot 0.8^2 = 160$
At time 3: $P_t = 250 \cdot 0.8^3 = 128$
At time 4: $P_t = 250 \cdot 0.8^4 = 102.4$

and so on