A housewife deposited Rs 10,000 on saving account at 5% p.a. interest compounded yearly and another sum on fixed deposit account at 8% p.a. interest compounded
half yearly. After one year the interest on fixed deposit account
was Rs 152.80 more
than the interest on the saving account, find the total amount of money in her two
accounts at the end of the year.

Rs. 3923.08

Step-by-step explanation:

First principal invested = Rs. 10000

Interest rate = 5%

The interest is compounded yearly.

Time = 1 year

1 year compound interest is equal to simple interest.

Formula for simple interest:

Interest on first sum =

Another sum is on fixed deposit 8% compounded half yearly.

Let the sum = Rs

Formula for compound interest is given as:

It is compounded half - yearly, therefore T = 2

As per question statement:

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

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