Symbolize and Solve Equations

Mathematics

1 answer:

NNADVOKAT [17]2 years ago

5 0

x = 5.43 + .83m

5.43 + .83 * 5 = 5.43 + 4.15 = $9.58

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A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

bija089 [108]

Answer: $\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}$

b) 5314

c) ln 2.7

d) 4.6 hrs

<u>Step-by-step explanation:</u>

$P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}$

$10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}$