Choose three options which are examples of exponential growth or decay.
A) The number in the sequence 2,6,24,120,720……
B) The amount of money in a bank account which earns compound interest.
C) The radioactivity of a sample of a radioactive isotope.
D) The savings of a person who saves £200 per month.
E) The temperature of water which is being heated in a kettle in a kettle to boiling point.
F) The numbers in the sequence 16,32,64,128,……
Are the three options B , E and C is this correct ??
Not E. That is linear. What about 2^n (F).
To identify examples of exponential growth or decay, you need to understand the characteristics of exponential functions.
Exponential growth is represented by the formula y = ab^x, where 'a' is a constant (the initial value), 'b' is the base (a positive number greater than 1), and 'x' is the exponent. The value of 'y' increases rapidly as 'x' increases.
Similarly, exponential decay is represented by the formula y = ab^x, where 'a' is a constant (the initial value), 'b' is the base (a positive number between 0 and 1), and 'x' is the exponent. The value of 'y' decreases rapidly as 'x' increases.
Now, let's analyze the given options:
A) The sequence 2, 6, 24, 120, 720... exhibits exponential growth since each term is obtained by multiplying the previous term by a constant value (in this case, 3). Therefore, option A is an example of exponential growth.
B) The amount of money in a bank account that earns compound interest is an example of exponential growth. As interest is continually added to the principal amount, the account balance increases at an increasing rate over time. So, option B is correct.
C) The radioactivity of a sample of a radioactive isotope is an example of exponential decay. The amount of radioactive material decreases over time at a rate proportional to the amount remaining. Thus, option C is also correct.
D) The savings of a person who saves £200 per month represents linear growth, not exponential. It increases steadily by a fixed amount each month rather than at an accelerating rate.
E) The temperature of water being heated in a kettle until boiling point represents linear growth, not exponential. The temperature rises steadily until it reaches the boiling point, without an accelerating rate of increase.
F) The sequence 16, 32, 64, 128... represents exponential growth because each term is twice the value of the previous term. So, option F is correct.
Therefore, the correct options for examples of exponential growth or decay are A, B, and C.