Growth and Depreciation

Growth

Growth refers to an increase in the value of a quantity over time, such as population, investment, or business revenue. It is often expressed as a percentage.

1. Population Growth Formula (Exponential Growth):

Where:

- \( P_T \) = Final population after growth 

- \( P_0 \) = Initial Population Value (starting amount) 

- \( R \) = Growth rate

- \( T\) = Time period 

2. Formula for \(R_1 %\), \(R_2 %\), \(R_3 %\) Population Growth Rate Every year:

Note: It’s every year so, \(T = 1\). 

3. Formula for Migrated in \(M_{in}\), Migrated out \(M_{out}\), Dead \(D\), Born \(B\):

Let us consider, in a particular year \(M_{in}\) and\(M_{out}\) people are migrated in and migrated out respectively. Also, \(D\) people are dead and \(B\) people are born. Then the population at the end of \(T\) years \(P_T\) is, given by,

Depreciation

Depreciation is the decrease in the value of an asset over time due to wear and tear, obsolescence, or usage.

1. Value Depreciation Formula (Exponential /Declining Balance Method)

Where:

- \( V_T\) = Value of asset after depreciation 

- \(V_0\) = Initial value (original cost) 

- \( R\) = Depreciation rate 

- \( T\) = Time period 

2. Formula for \(R_1 %\), \(R_2 %\), \(R_3 %\) Value Depreciation Rate Every year:

Note: It’s every year so, \(T = 1\). 

Practice Questions Growth and Depreciation SEE

Growth

1. The population of a village is 10,000. The population grows by 2% annually in the village. [SEE O80 SP]

1. Write the formula used to find the population after T years. [1K]
2. After how many years the population of the village will be 10,404? Find it. [2U]
3. If the population increases at the rate of 4% per annum, by what number will the population of that village be increased in 2 years? Find it. [1A]

2. The population of a city before three years was 25,00,000. The annual population growth rate of the city is 5%. One year ago, 74,000 people migrated to other places and 1,000 died due to desease. [SEE 080 MP]

1. What is the rate of annual compound growth? Write it. [1K]
2. Find the population of the city before two years. [2A]
3. Compare the present population and the population before 3 years of the city. Then write the conclusion. [2HA]

Depreciation

3. A photocopy machine is purchased for Rs. 80,000. After using for 2 years, only Rs. 30,000 is earned. The price of the machine depreciates annually at the rate of 20% and the machine is sold after 2 years. [SEE O80 C]

1. Find the selling price of the machine after 2 years. [1A]
2. Find the total profit or loss in percentage on selling the machine. [2HA]

4. A machinery good bought for Rs. 1,00,000 depreciates by 10% in the first 2 years and then by 5% in the next 1 year. [SEE MODEL]

1. Find the price after 1 year. [1U]
2. What will be the price after 3 years? [2A]
3. If the depreciation rate of two years and that of the next one year are exchanged, then what would be the difference in the price after 3 years? [2HA]