The Problem**:**

The number of flu viruses in Jake's body is growing exponentially. At noon ( t = 0 ), the number of flu viruses in Jake's body was one million. At 2 PM ( t = 2 ), the number of viruses in Jake's body was 2 million. How many flu viruses will inhabit Jake's body at 6 PM ( t = 6 )? |

The solution**:**

Let Q(t) equal the number of flu viruses in Jake's body t hours after noon. Exponential growth of Q(t) implies that Q(t) = Q _{o} e^{kt}Substituting t = 0 , we find (1 million) = Q _{o} e^{k(0)} = Q_{o}(1) = Q_{o}Thus, for any t, Q(t) = (1 million) e ^{kt}Substituting t = 2 , we find (2 million) = (1 million) e,^{k(2)}and thus e = 2^{k(2)}We could now find the value of "k", but this is unnecessary We seek Q(t) at 6 PM ( t = 6 ) Substituting t = 6 , we find Q(6) = (1 million) e ^{k(6)}= (1 million) e^{k(2)} = (1 million) [^{(3)}e]^{k(2)}^{3}= (1 million) [ 2 ^{3}] = 8 millionThus Jake's body holds 8 million flu viruses at 6 PM |