Some radioactive isotopes decay at an exponential rate. This decay can be modeled through the function At = A0 e-rt, where At is the mass at any time t, A0 is the original amount, r is the decay rate constant, and t is the time. In addition, each radioactive isotope has a half-life, which is the time it takes for an amount of the material to decrease by half. Using this equation, derive an equation that can be used to calculate the half-life of a certain material.

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answer: it's d

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answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)