Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $n ! = 10 \mathrm {~K}$, where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$.
Evaluate 95 ! using the approximation given above.
A) $1.059 \times 10 ^ { 147 }$
B) $1.032 \times 10 ^ { 148 }$
C) $1.087 \times 10 ^ { 394 }$
D) $1.480 \times 10 ^ { 2 }$

Question

Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $n ! = 10 \mathrm {~K}$, where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$. 
Evaluate 95 ! using the approximation given above.
A) $1.059 \times 10 ^ { 147 }$
B) $1.032 \times 10 ^ { 148 }$
C) $1.087 \times 10 ^ { 394 }$
D) $1.480 \times 10 ^ { 2 }$

Quizplus · Accepted Answer

Using the approximation formula, calculate K for n = 95, then compute 10^K to find the approximate value of 95!.

Many Calculators or Computers Cannot Directly Calculate 70 ! or Higher