Subjects algebra

Sales Growth Eef44F

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1. **State the problem:** We are given the formula for sales $C$ as a function of $N$: $$C = 240 \cdot 4^{N - 1}$$ and we want to understand how sales change with $N$. 2. **Formula explanation:** This is an exponential growth formula where $240$ is the initial sales when $N=1$, and sales multiply by $4$ for each increase in $N$ by 1. 3. **Calculate sales for specific values:** - For $N=1$: $$C = 240 \cdot 4^{1-1} = 240 \cdot 4^0 = 240 \cdot 1 = 240$$ - For $N=2$: $$C = 240 \cdot 4^{2-1} = 240 \cdot 4^1 = 240 \cdot 4 = 960$$ - For $N=3$: $$C = 240 \cdot 4^{3-1} = 240 \cdot 4^2 = 240 \cdot 16 = 3840$$ - For $N=4$: $$C = 240 \cdot 4^{4-1} = 240 \cdot 4^3 = 240 \cdot 64 = 15360$$ - For $N=5$: $$C = 240 \cdot 4^{5-1} = 240 \cdot 4^4 = 240 \cdot 256 = 61440$$ - For $N=6$: $$C = 240 \cdot 4^{6-1} = 240 \cdot 4^5 = 240 \cdot 1024 = 245760$$ - For $N=7$: $$C = 240 \cdot 4^{7-1} = 240 \cdot 4^6 = 240 \cdot 4096 = 983040$$ 4. **Interpretation:** Sales increase by a factor of 4 each time $N$ increases by 1, showing exponential growth. **Final answer:** The sales for each $N$ follow the formula $$C = 240 \cdot 4^{N - 1}$$ with values as calculated above.