Subjects algebra

Exponential Check 574B22

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1. **State the problem:** We are given points from an exponential function and Saraid's proposed equation $y=125(1.25)^x$. We need to check if this equation correctly represents the data. 2. **Recall the general form of an exponential function:** $$y = a b^x$$ where $a$ is the initial value (when $x=0$) and $b$ is the base or growth/decay factor. 3. **Identify $a$ from the table:** When $x=0$, $y=125$. So, $a=125$. 4. **Check Saraid's $a$-value:** Saraid's $a=125$ matches the table, so $a$ is correct. 5. **Find $b$ using two points:** Use points $(1,100)$ and $(0,125)$: $$100 = 125 \times b^1$$ Divide both sides by 125: $$\frac{100}{125} = \cancel{125} b^1 / \cancel{125}$$ $$0.8 = b$$ 6. **Check Saraid's $b$-value:** Saraid's $b=1.25$ but calculation shows $b=0.8$. 7. **Verify with another point:** Using $(2,80)$: $$80 = 125 \times 0.8^2 = 125 \times 0.64 = 80$$ This confirms $b=0.8$ is correct. **Final conclusion:** - Saraid's $a$-value is correct. - Saraid's $b$-value is incorrect; it should be $0.8$ instead of $1.25$. **Answer:** The $a$-value in Saraid's equation is correct, but the $b$-value is wrong and should be $0.8$.