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
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