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bazaltina [42]
3 years ago
12

The mass of bacteria in a labaratory experiment increases exponentially by 22% each hour. The mass of bacteria was 8 micrograms

when the experiment began. You are interested in predicting how long it will take for the mass of bacteria to reach 100 micrograms.
Mathematics
1 answer:
den301095 [7]3 years ago
5 0

Answer:

The Answer is approximately 12.71 seconds.

Step-by-step explanation:

The form of the equation is:

f(x) = ab^x

Substitute:

f(x) = 8(1.22)^x

Solve for:

f(x) = 100

100 = 8(1.22)^x

100/8 = 1.22^x

12.5 = 1.22^x

1.22^x = 12.5

log(1.22^x) = log(12.5)

x * log(1.22) = log(12.5)

x * 0.0863 = 1.0969

x = 1.0969 / .0863 = 12.71 seconds, approximately

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Answer:

\large\boxed{x=\dfrac{5}{4},\ y=\dfrac{15}{16}}

Step-by-step explanation:

\left\{\begin{array}{ccc}y=\dfrac{3}{4}x&(1)\\\dfrac{5}{2}x+2y=5&(2)\end{array}\right\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\\dfrac{5}{2}x+2\left(\dfrac{3}{4}x\right)=5\\\\\dfrac{5}{2}x+\dfrac{3}{2}x=5\\\\\dfrac{5+3}{2}x=5\\\\\dfrac{8}{2}x=5\\\\4x=5\qquad\text{divide both sides by 4}\\\\x=\dfrac{5}{4}

\text{Put the value of}\ x\ \text{to (1)}\\\\y=\dfrac{3}{4}\cdot\dfrac{5}{4}\\\\y=\dfrac{15}{16}

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Step-by-step explanation:

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Step-by-step explanation:

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