Laws of Indices (SP4.2)

Front

What is the formula for compound interest?

Back

P = f(1 + r)^t, where P is the final amount, f is the initial investment, r is the annual interest rate, and t is the time in years.

Front

How do you calculate the amount of bacteria after t minutes if it doubles every minute?

Back

The amount of bacteria is given by the formula: Initial amount × (2^t).

Front

If Mr. Lee invests RM 50,000 at an 8% interest rate, what is the investment amount after 20 years?

Back

RM 233,048.

Front

What does the term 'exponential growth' refer to in the context of bacteria multiplication?

Back

Exponential growth occurs when the quantity increases by a consistent percentage over a period of time, leading to rapid growth.

Front

What is the value of 2^10?

Back

1024.

Front

If a population of bacteria is 200 and doubles every minute, how many bacteria will there be after 5 minutes?

Back

6,400 bacteria.

Front

What is the significance of the base in an exponential function?

Back

The base determines the growth rate; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you solve for t in the equation 200(2^t) = 819200?

Back

Divide both sides by 200 to get 2^t = 4096, then solve for t: t = 12.

Front

What is the relationship between the interest rate and the final amount in compound interest?

Back

A higher interest rate results in a greater final amount due to the effect of compounding.

Front

What does 't' represent in the context of the formulas provided?

Back

't' represents the time in years or minutes, depending on the context of the problem.