Exponential equation word problem

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The doubling time for a certain skin bacteria is 1.8 hours. There are 1000 bacteria per 1 square centimeter on your phone, and 100 square centimeters in contact with your face.

  1. Write the general equation.

  2. Find the amount of bacteria on your face after 2 hours after taking a call.

My solution:

$1.$

$doubling time={ln 2}/{k}$

$1.8={ln2}/{k}$

$k=0.39$

$N={N_0}e^{0.39t}$

$N={1000*bacteria}*{cm^{-1}}{100cm}^{2}*{e}^{0.39t}$

$N=100000*e^{0.39t}$

$2.$

$N=100000*bacteria*e^{0.39*2}=218147=220000*bacteria$

Is this okay for the "general" equation?

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Your approach looks fine to me, you just need to be careful with approximating $k$ because it's in the exponent. I get around $216,000$ bacteria after $2$ hours. You can also use $\Large{N=N_0 2^{\frac{t}{1.8}}}$ as the general equation