A bacteria culture starts with 500 bacteria and doubles in size every 6 hours. How do you find an exponential model for t?

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Answer 1 · 2017-09-25T12:34:27

Exponential model of bacteria growth at time $t$ $t$ is
$B_{t} = 500 \cdot e^{0.115525 t}$ $B_t= 500 *e^(0.115525t)$

Starting number of bacteria is $B_{0} = 500$ $B_0 = 500$ , It doubles in

size every $6$ $6$ hours. Number of bacteria after $t = 6$ $t=6$ hours

grows to $B_{6} = B_{0} \cdot 2 = 500 \cdot 2 = 1000$ $B_6=B_0*2=500*2=1000$ . The exponential growth

formula is $B_{t} = B_{0} \cdot e^{k t}$ $B_t= B_0 *e ^(kt)$ , where $k$ $k$ is growth rate

$:. e^(kt) = B_t/B_0 or e^(kt) = 1000/500=2$ Taking natural

log on both sides we get $ln e^(kt) = ln 2 or kt= ln 2$ (since

$ln e^(kt)=kt$ ) $:. k =ln2/t=ln 2/6 or k ~~ 0.115525$

Exponential model of bacteria growth at time $t$ is

$B_t= 500 *e^(0.115525t)$ [Ans]