Rewriting Exponential Functions Answers
Which of the following functions represent exponential growth?
Which of the following functions represent exponential decay?
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?
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
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.
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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.
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Abel is years older than Zöe.
3
Choose the equation that relates the balances in the accounts y years after Martin opened his account.
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
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