Exponential&Logarithmics

Front

What is the formula for calculating simple interest?

Back

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) / 100

Front

What is the logarithmic form of the equation 2^3 = 8?

Back

log₂8 = 3

Front

What is the y-intercept of the exponential function y = 2^x?

Back

The y-intercept is (0, 1) because 2^0 = 1.

Front

How do you express a population decrease of 6% per year mathematically?

Back

Population after t years = Initial Population × (1 - 0.06)^t

Front

What is the general form of an exponential growth equation?

Back

y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What does the base of a logarithm represent?

Back

The base of a logarithm indicates the number that is raised to a power to obtain a given number.

Front

Convert the logarithmic equation log₃81 = 4 to exponential form.

Back

3^4 = 81

Front

If a quantity doubles every year, what is the growth factor?

Back

The growth factor is 2.

Front

What is the relationship between exponential functions and their inverses?

Back

The inverse of an exponential function is a logarithmic function.

Front

How do you find the population after 10 years if it decreases by 6% annually?

Back

Use the formula: Final Population = Initial Population × (0.94)^10.