Subjects algebra

Growth Parameters 0Ce732

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1. The problem gives the exponential growth function $$Q = 79(1.002)^t$$ and asks to identify the starting value $a$, the growth factor $b$, and the growth rate $r$ as a percent. 2. The general form of the exponential growth function is $$Q = ab^t = a(1 + r)^t$$ where: - $a$ is the starting value (initial amount), - $b$ is the growth factor, - $r$ is the growth rate expressed as a decimal. 3. From the given function, we can directly compare: - $a = 79$ - $b = 1.002$ 4. Since $b = 1 + r$, we solve for $r$: $$r = b - 1 = 1.002 - 1 = 0.002$$ 5. To express $r$ as a percent, multiply by 100: $$r = 0.002 \times 100 = 0.2\%$$ 6. Therefore, the correct values are: - $a = 79$ - $b = 1.002$ - $r = 0.2\%$ 7. Comparing with the options, choice A matches these values exactly. Final answer: **A**