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saveliy_v [14]
1 year ago
5

A bacteria population grows by 10% every 2 years. Presently, the population is 80 000 bacteria. Find the population in 8 years f

rom now. (Can use log if needed but not “in”)
Mathematics
1 answer:
faust18 [17]1 year ago
3 0

An exponential function is modeled using the equation:

P(t)=a(1+r)^{\frac{t}{n}}

where P(t) is the population after t years, a is the initial population, r is the growth rate in decimals, t is the number of years, and n is the number of periods in one cycle.

From the given information, we have the following parameters:

\begin{gathered} a=80000 \\ r=0.1 \\ t=8 \\ n=2 \end{gathered}

Therefore, the population after 8 years can be calculated by substituting into the formula and solving for P(t) as follows:

\begin{gathered} P(t)=80000(1+0.1)^{\frac{8}{2}}=80000(1.1)^4 \\ P(t)=117128 \end{gathered}

The population is 117,128.

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2 years ago
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3 years ago
(a) A lamp has two bulbs, each of a type with average lifetime 1400 hours. Assuming that we can model the probability of failure
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Answer:

For first lamp ; The resultant probability is 0.703

For both lamps; The resultant probability is 0.3614

Step-by-step explanation:

Let X be the lifetime hours of two bulbs

X∼exp(1/1400)

f(x)=1/1400e−1/1400x

P(X<x)=1−e−1/1400x

X∼exp⁡(1/1400)

f(x)=1/1400 e−1/1400x

P(X<x)=1−e−1/1400x

The probability that both of the lamp bulbs fail within 1700 hours is calculated below,

P(X≤1700)=1−e−1/1400×1700

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The resultant probability is 0.703

Let Y be a lifetime of another lamp two bulbs

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X+Y=Z∼gamma(2,1/1400)

2λZ∼

X+Y=Z∼gamma(2,1/1400)

2λZ∼χ2α2

The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,

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3 years ago
A 3 cm x 3 cm rectangle sits inside a circle with radius of 4 cm.
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Given:

Rectangle inside a circle.

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Width of a rectangle = 3 cm

Area of a rectangle = length × width

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Area of a rectangle = 9 cm²

Radius of a circle = 4 cm

Area of a circle = πr²

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Area of a circle = 50.24 cm²

Area of shaded region = Area of circle - Area of rectangle

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The area of the shaded region is 41.24 cm².

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