Rewriting Exponential Functions Answers
Which of the following functions represent exponential growth?
Which of the following functions represent exponential decay?
Combine the first two equations and laws of exponents to find the equation for the mass of sodium remaining after y years.
Approximately how many milligrams of sodium remain after 8.4 years? ✔ 85.2 mg95.2 mg247.6 mg645.5 mg
Choose the pair of expressions that describe the accounts y years after Martin opened his account.
Which expression represents the mass of sodium remaining after h half-lives?
Is this exponential growth or decay? Explain using your understanding of the properties of exponents. (To type exponents, use the ^ key.)
This is exponential decay. The property of negative exponents states that a^(-n) = 1/a^n, so 2^(-t/8) can be rewritten as (1/2)^(t/8) or 0.5^(t/8). Because the base (0.5) is between 0 and 1, the function represents decay.
What is the half-life for the zombie population? Explain in terms of exponents. (To type an exponent, use the ^ key.)
To find the half-life, the exponential part of the function (0.5)^(t/8) needs to equal 0.5. This happens when the exponent t/8 equals 1. Solving for t, we get t = 8. Therefore, the half-life is 8 units of time (such as hours or days), because at t = 8, the base of 0.5 is raised to the power of 1, resulting in half of the initial population.
years older than Zöe.
3
Choose the equation that relates the balances in the accounts y years after Martin opened his account.
Which expression relates h, the number of half-lives, and y, the number of years?h = 2.6 + yh = 2.6 – yh = 2.6y✔ h = y/2.6
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Check all facts you included in your answer.
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