Question

According to the manual, a battery in a cellular phone loses 2% of its charge each day. Assume the battery is 100% charged.

a) Write an equation to represent the percent charge, P, as a function of the number of days, d, since the battery was charged.

b) Determine the number of days until the battery in only 50% charged.

Answer 1

Ok, after day 1, what percentage is the battery charged? 98% What's that as a fraction?

Answer 2

49/50

Answer 3

Good and as a decimal it's 0.98

Now what's the charge after two days? It is *not* 1 - 0.02 -0.02 = 0.96. It is something else. What is it?

Answer 4

It is 98% of what was available on day 1. I.e., 98% of 98%.

That is, it is
(0.98)(0.98) = (0.98)^2

Answer 5

make sense?

Answer 6

ya

Answer 7

Hence what is the charge after 3 days?

Answer 8

(0.98)^2 (0.98)

Answer 9

Yes, which can be simplified to what?

Answer 10

0.941192

Answer 11

No, I mean it can be simplified to (0.98)^3

What is the charge therefore after n days? It is
(0.98)^n

To answer the last part of your question, you have to find the n such that
(0.98)^n = 0.5
or the integer for which (0.98)^n is just less than 0.5

For that you will need logarithms.

Answer 12

0.5^2

Answer 13

=0.25