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The radioactive substance uranium-240 has a half-life of 14 hours. The amount At of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponential function.
[tex]A(t) = 2800.(\frac{1}{2})^{\frac{t}{14}}[/tex]
Find the amount of the sample remaining after 9 hours and after 40 hours.
Round your answers to the nearest gram as necessary.
Amount after 9hours: ______ grams
Amount after 40 hours: ______ grams

Respuesta :

Answer:

Amount after 9 hours: 1793 grams

Amount after 40 hours: 386 grams

Step-by-step explanation:

Given exponential function, that shows the amount of radioactive substance uranium-240 after t hours,

[tex]A(t)=2800(\frac{1}{2})^\frac{t}{14}[/tex]         ......(1)

Substitute t=9 in equation (1),

The amount of substance after 9 hours is,

[tex]A(9)=2800(\frac{1}{2} )^\frac{9}{14}[/tex]

≈ 1793 grams ( Using calculator )

Again, substitute t=40 in equation (1),

The amount of substance after 40 hours is,

[tex]A(40)= 2800(\frac{1}{2})^{\frac{40}{14} }[/tex]

≈ 386 grams.

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