Exponential&Logarithmics

Front

What is the formula for calculating simple interest?

Back

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

Tags

CCSS.6.EE.B.6

Front

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

Back

log₂8 = 3

Tags

CCSS.HSF.BF.B.5

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

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.

Tags

CCSS.HSF-IF.C.8B

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

Tags

CCSS.HSF.BF.B.5

Front

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

Back

The growth factor is 2.

Tags

CCSS.HSF-LE.A.1C

Front

What is the relationship between exponential functions and their inverses?

Back

The inverse of an exponential function is a logarithmic function.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-LE.A.1C