To write an exponential equation in the form \( y = a(b)^x \) that models the expected monthly number of albums sold by Lily Starbright, we begin by identifying the initial parameters:
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Initial Value (a): This is the number of albums sold in the first month (March). Lily sold 1,040 copies by the end of March, so we take: \[ a = 1040 \]
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Growth Factor (b): To determine the growth factor, we need to compare the sales from March to April. The sales in April were 1,352 copies. The growth can be calculated as follows: \[ \text{Growth Factor} = \frac{\text{Sales in April}}{\text{Sales in March}} = \frac{1352}{1040} \] Let's calculate this value: \[ \frac{1352}{1040} \approx 1.298076923 \] We can round this value to 1.30 for simplicity, which indicates a percentage increase of about 30%.
Now, we can formulate the equation. Let \( x \) be the number of months after the release:
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For March (the first month), \( x = 0 \), so: \[ y = 1040(1.30)^0 = 1040 \]
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For April (the second month), \( x = 1 \): \[ y = 1040(1.30)^1 \approx 1352 \]
Putting this all together, the exponential model that represents the expected monthly sales can be written as: \[ \boxed{y = 1040(1.30)^x} \]
This equation will model the expected number of albums sold \( y \) \( x \) months after the album's release.