A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential

Question

A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula P = C 2 r t gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r ?

Accepted Answer

Choice B is correct. It&rsquo;s given that the formula P = C 2 r t gives the number of bacteria in a growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. It&rsquo;s also given that a scientist initially measures 12,000 bacteria in the growth medium. Since the initial measurement is 0 hours after the initial measurement, it follows that when t = 0 , P = 12,000 . Substituting 0 for t and 12,000 for P in the given equation yields 12,000 = C 2 r 0 , or 12,000 = C 2 0 , which is equivalent to 12,000 = C . It&rsquo;s given that 4 hours later, the scientist measures 24,000 bacteria, or when t = 4 , P = 24,000 . Substituting 4 for t , 24,000 for P , and 12,000 for C in the given equation yields 24,000 = 12,000 2 4 r . Dividing each side of this equation by 12,000 yields 2 = 2 4 r , or 2 1 = 2 4 r , which is equivalent to 1 = 4 r . Dividing both sides of this equation by 4 yields 1 4 = r . Therefore, the value of r is 1 4 . Choice A is incorrect. This is the value of the reciprocal of C . Choice C is incorrect. This is the value of the reciprocal of r . Choice D is incorrect. This is the value of C .

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