In order to save one million naira for the purchase of some goods a man save #1,#2,#4 #8 on the first,second,third and fourth day respectively.At this rate assuming that no interest was added
(a):what amount was saved on the 15th day?
(b):at least how many days were needed to accumulate the one million naira?....plz help
first day -- 1 = 2^0
2nd day -- 2 = 2^1
3rd day -- 4 = 2^2
..
15th day ---- 2^14 or 16384
accumulate means you want the sum to be 1 million
we have a geometric series with
a = 1
r = 2
n = ??
sum(n) = 1000000
sum(n) = a(r^n - 1)/(r-1)
1000000 = 1(2^n - 1)/1
2^n = 1000001
take log of both sides and use log rules
n log2 = log 1000001
n = 19.93
so 19 days are not enough, so it must be 20 days
To determine the amount saved on the 15th day, we can look for a pattern in the amount saved each day.
On the first day, the amount saved is #1.
On the second day, the amount saved is #2.
On the third day, the amount saved is #4.
On the fourth day, the amount saved is #8.
We can see that each day, the amount saved is doubling. This means that the amount saved on the 15th day will be double the amount saved on the 14th day.
To find the amount saved on the 15th day, we can start by finding the amount saved on the 14th day and then double it.
On the 14th day, the amount saved is #8 * 2 = #16.
Therefore, the amount saved on the 15th day is #16 * 2 = #32.
(a) The amount saved on the 15th day is #32.
To determine the number of days needed to accumulate one million naira, we need to divide the total amount needed by the daily amount saved.
Since we know that the person is saving in naira, we need to convert one million naira to the equivalent amount in the local currency.
Given that 1 naira is equivalent to #100, we can calculate the total amount needed as:
1,000,000 naira * #100 = #100,000,000.
Now we can divide the total amount needed by the daily amount saved to find the number of days needed.
#100,000,000 / #32 = 3,125,000.
Therefore, at least 3,125,000 days are needed to accumulate one million naira.
(b) At least 3,125,000 days are needed to accumulate the one million naira.
To find the amount saved on the 15th day, we need to find the pattern in the savings for each day. Looking at the sequence provided, we can see that each day's saving is double the amount saved on the previous day.
Let's calculate the savings for the first few days to observe the pattern:
Day 1: #1
Day 2: #2 = 2 * #1
Day 3: #4 = 2 * #2
Day 4: #8 = 2 * #4
From the observations, we can deduce that for any given day, the saving will be double the previous day's saving. Therefore, we can use the formula:
Saving on the nth day = 2^(n-1) * initial saving
Now, let's calculate the amount saved on the 15th day using this formula:
Saving on the 15th day = 2^(15-1) * #1 = 2^14 * #1
To evaluate this expression, we need to know the value of #1. Since it is not mentioned in the question, we cannot calculate the exact amount saved on the 15th day without that information.
Moving on to part (b), we need to determine how many days are needed to accumulate one million naira.
To find the number of days required, we need to use a reverse approach. Starting with the initial saving amount (#1), we need to find how many times we need to double this amount to reach one million naira.
Let's set up the equation:
#1 * 2^(n-1) = 1,000,000
Here, n represents the number of days needed to accumulate one million naira.
Taking the logarithm base 2 on both sides of the equation, we get:
n - 1 = log2(1,000,000 / #1)
Rearranging the equation, we have:
n = 1 + log2(1,000,000 / #1)
To find the minimum number of days, we need to round up the result since we can only have whole, non-fractional days.