To evaluate the function \( R(t) = 3000 - 500 \times 1.4^t \) for \( t \) values from 0 to 6, we'll substitute each value of \( t \) into the equation and calculate the corresponding \( R(t) \).
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For \( t = 0 \): \[ R(0) = 3000 - 500 \times 1.4^0 = 3000 - 500 \times 1 = 3000 - 500 = 2500 \]
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For \( t = 1 \): \[ R(1) = 3000 - 500 \times 1.4^1 = 3000 - 500 \times 1.4 = 3000 - 700 = 2300 \]
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For \( t = 2 \): \[ R(2) = 3000 - 500 \times 1.4^2 = 3000 - 500 \times 1.96 = 3000 - 980 = 2020 \]
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For \( t = 3 \): \[ R(3) = 3000 - 500 \times 1.4^3 = 3000 - 500 \times 2.744 = 3000 - 1372 = 1628 \]
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For \( t = 4 \): \[ R(4) = 3000 - 500 \times 1.4^4 = 3000 - 500 \times 3.8416 = 3000 - 1920.8 = 1079.2 \]
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For \( t = 5 \): \[ R(5) = 3000 - 500 \times 1.4^5 = 3000 - 500 \times 5.378 = 3000 - 2689 = 311 \]
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For \( t = 6 \): \[ R(6) = 3000 - 500 \times 1.4^6 = 3000 - 500 \times 7.529 = 3000 - 3764.5 = -764.5 \]
Now we can summarize the results for each value of \( t \):
- \( R(0) = 2500 \)
- \( R(1) = 2300 \)
- \( R(2) = 2020 \)
- \( R(3) = 1628 \)
- \( R(4) = 1079.2 \)
- \( R(5) = 311 \)
- \( R(6) = -764.5 \)
Would you like to do anything else with these results?