Math  /  Algebra

Question15 Mark for Review
In a certain nuclear chain reaction, the number of atoms increases. At time 700 miliseconds since the start of the reaction, there are about 1500 atoms, and at time 770 milliseconds, there are about 3000 atoms. Using a logarithmic regression, a model TT is constructed, where T(x)=a+blnxT(x)=a+b \ln x gives the time, in milliseconds, at which there are xx atoms. Which of the following best approximates the number of milliseconds it will take for the number of atoms to reach 10,000 ? (A) 891 (B) 930 (C) 1097 (D) 1201

Studdy Solution
Use the model to find the time for 10,000 atoms.
Substitute x=10000 x = 10000 into the model: T(10000)=a+bln(10000) T(10000) = a + b \ln(10000)
Substitute the values of a a and b b : T(10000)=(70070ln(2)ln(1500))+70ln(2)ln(10000) T(10000) = \left(700 - \frac{70}{\ln(2)} \ln(1500)\right) + \frac{70}{\ln(2)} \ln(10000)
Calculate T(10000) T(10000) using the values: T(10000)891 T(10000) \approx 891
Therefore, the number of milliseconds it will take for the number of atoms to reach 10,000 is approximately:
891 \boxed{891}

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