**Using percent of change:**

Given an original amount and a percent increase or decrease, you can use the percent of change to find the new amount.

**Example 1 : **

The grizzly bear population in Yellowstone National Park in 1970 was about 270. Over the next 35 years, it increased by about 115%. What was the population in 2005 ?

**Solution :**

**Step 1 : **

Find the amount of change.

Find 115% of 270. Write 115% as a decimal.

1.15 × 270 = 310.5

Round to the nearest whole number.

≈ 311

**Step 2 : **

Find the new amount.

New Amount = Original Amount + Amount of Change

Substitute values and add them.

= 270 + 311

= 581

Hence, the population in 2005 was about 581 grizzly bears.

**Example 2 : **

Mr. David is running a business firm and he made $12000 profit last year. If the profit for this year is 20% less than the last year, find the profit for this year.

**Solution :**

**Step 1 : **

Find the change in profit.

Find 20% of 12000. Write 20% as a decimal.

0.20 × 12000 = 2400

**Step 2 : **

Find the profit for this year .

Since the profit is decreased, we have to subtract the change in profit ($2400) from the profit of the last year ($12000).

Profit for this year is

= Profit for the last year - Change in profit

Substitute values and subtract them.

= 12000 - 2400

= 9600

Hence, the profit for this year is $9600.

**Example 3 : **

If an amount of $100 in a savings account increases by 10%, then increases by 10% again, is that the same as increasing by 20% ?

**Solution :**

**Case (i) : **Given amount is increased by 10% and again by 10%

Find the amount of change for the first 10%.

Find 10% of 100. Write 10% as a decimal.

0.10 × 100 = 10

New amount after the first increment of 10% is

= Original Amount + Amount of Change

= 100 + 10

= 110

Increased again by 10%.

Find 10% of 110. Write 10% as a decimal

0.10 x 110 = 11

New amount after the second increment of 10% is

= 110 + 11

= 121 -----> (1)

**Case (ii) : **Given amount is increased by 20%.

Find the amount of change.

Find 20% of 100. Write 20% as a decimal.

0.20 × 100 = 20

New amount after the increment of 20% is

= Original Amount + Amount of Change

= 100 + 20

= 120 -----> (2)

**Conclusion :**

From (1) and (2), it is clear that increasing an amount by 10%, then increases by 10% again is not the same as increasing by 20%.

After having gone through the stuff given above, we hope that the students would have understood "Using percent of increase or decrease".

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