Unit 7 Flexible Practice

Classify $3,8,13,18$.

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Explain why this conclusion is valid: Exponential ratio $3$. Use the foundation problem as evidence: Values $5,15,45,135$.

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Create a nearby example by changing one number or condition in this prompt: Multiplier for $7\%$ growth. Predict the effect, solve your new example, and compare it with the original.

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Domain of $5(0.4)^x$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is calling $b$ itself the percentage rate.

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HA of $4^x+3$.

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Explain why this conclusion is valid: HA $y=4,$ range $(-∞,4),$ point $(1,1)$. Use the foundation problem as evidence: Analyze $-3\cdot 2^(x-1)+4$.

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Create a nearby example by changing one number or condition in this prompt: Rewrite $9^(\frac{x}{2})$. Predict the effect, solve your new example, and compare it with the original.

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$50$ doubles every $8$ days.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is mixing time units or using $6$ instead of $1.06$ for $6$ percent growth.

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Formula at $5\%$ annual.

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Explain why this conclusion is valid: $A=2000(1.005)^36\approx 2393.36$. Use the foundation problem as evidence: $\$2000$ at $6\%$ monthly for $3$ years.

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Create a nearby example by changing one number or condition in this prompt: Periods in $7$ years monthly. Predict the effect, solve your new example, and compare it with the original.

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Approximate $e$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is interpreting $k=0.06$ as exactly $6$ percent effective growth.

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Residual observed $20,predicted 22.5$.

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Solve the representation example, then name the feature of exponential regression and residuals that it illustrates: Interpret$$b=0.81$$

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Write a short verification checklist for exponential regression and residuals, then apply it to one worked example from this lesson.

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Can standard model exceed K?

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Connect two representations for this example: $P=\frac{1000}{1+9e^(-0.4t)}$. Describe what a graph, table, mapping, or algebraic form would have to show.

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$$log_2(1)$$

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Solve the representation example, then name the feature of logarithms as inverse functions that it illustrates$$log_2(1)$$

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Write a short verification checklist for logarithms as inverse functions, then apply it to one worked example from this lesson.

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Range of $4lnx+8$.

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Connect two representations for this example: Analyze $log_3(4-2x)$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Expand$$log_b(\frac{x}{y})$$

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Solve the representation example, then name the feature of logarithm laws that it illustrates: Expand$$log_b(\frac{x}{y})$$

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Write a short verification checklist for logarithm laws, then apply it to one worked example from this lesson.

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Can $2^x=-4$ have real solution?

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Connect two representations for this example: Solve $3^x=10$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Solve$$ln(x-2)=0$$

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Solve the representation example, then name the feature of solving logarithmic equations and interpreting inverse models that it illustrates: Solve$$ln(x-2)=0$$

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