Exponential Review

Front

What is the Quotient Rule in Exponential Functions?

Back

The Quotient Rule states that if you have a function that is the quotient of two other functions, then the derivative of that function is given by: \( \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2} \) where u and v are functions of x.

Front

Evaluate the expression using the Quotient Rule: \( \frac{x^{13}}{x^8} \)

Back

Using the Quotient Rule, \( \frac{x^{13}}{x^8} = x^{13-8} = x^5 \)

Front

What is the formula for Compound Interest?

Back

The formula for compound interest is: \( A = P(1 + r/n)^{nt} \) where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

Calculate the total amount in the account after 8 years if $360 is invested at an interest rate of 5.5% compounded annually.

Back

Using the compound interest formula: \( A = 360(1 + 0.055/1)^{1*8} = 360(1.055)^8 \approx 552.49 \)

Front

If Jacob borrows $500 at an interest rate of 2.5% compounded annually for 5 years, how much will he owe?

Back

Using the compound interest formula: \( A = 500(1 + 0.025/1)^{1*5} = 500(1.025)^5 \approx 565.70 \)

Front

What is the Power Rule in Exponential Functions?

Back

The Power Rule states that if you have a function \( f(x) = x^n \), then the derivative is given by: \( f'(x) = nx^{n-1} \).

Front

Simplify the expression: \( \frac{-1}{3x^5y^7} \)

Back

The expression is already simplified as \( \frac{-1}{3x^5y^7} \).

Front

What is the product of two exponential expressions with the same base?

Back

When multiplying two exponential expressions with the same base, you add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

What is the result of \( \frac{b^6}{2a^2} \) when simplified?

Back

The expression is already simplified as \( \frac{b^6}{2a^2} \).

Front

What happens when you divide two exponential expressions with the same base?

Back

When dividing two exponential expressions with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).