Assume That a Culture of Bacteria Grows at a Rate $10 ^ { 6 }$

Short Answer

Assume that a culture of bacteria grows at a rate proportional to its size such that if $10 ^ { 6 }$ bacteria are present initially, then there are 2 × $10 ^ { 6 }$ bacteria present after 3 hours. Determine a formula for the number of bacteria present after t hours in terms of powers of 2. (Hint: Recall that $b ^ { x }$ = $\mathrm { e } ^ { ( \ln b ) x }$ .)Enter your answer exactly in the form $\mathrm { P } ( \mathrm { x } ) = \mathrm { a }^ b \cdot 2 ^{\mathrm { c } / \mathrm { d }}$