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Sladkaya [172]
3 years ago
14

What type of number can be written as an a fraction a/b where a and b are Integres and b is not equal to zero?

Mathematics
1 answer:
faltersainse [42]3 years ago
6 0

Answer:

Integers, Terminating Decimals, Recurring Decimals, Proper and Improper Fractions.

Step-by-step explanation:

The following subset of the real number system can be written in the form \dfrac{a}{b}, b≠0.

Integers(ℤ): These are positive and negative whole numbers. For example, 5 can be written as \dfrac{5}{1}

Terminating Decimals: These are fractions that when converted to decimal numbers have an end.

e.g. \dfrac{5}{2}=2.5

Recurring Decimals: These are fractions that when converted to decimal numbers do not have an end.

e.g. \dfrac{8}{11}=0.727272...=0.\overline{72}

Proper Fractions: These are fractions of the form \dfrac{a}{b} where a<b. An examples is \dfrac{4}{5}

Improper Fractions: These are fractions of the form \dfrac{a}{b} where a>b. An examples is \dfrac{5}{4}

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Step-by-step explanation:

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<em><u>Solution:</u></em>

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

<em><u>The increasing function is given as:</u></em>

y = a(1+r)^t

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

r = 80 \5 = \frac{80}{100} = 0.8

<em><u>Determine how many will be in 5 hours</u></em>

Substitute t = 5

y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96

y = 189

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<em><u>Determine how many will be in 1 day ?</u></em>

1 day = 24 hours

Substitute t = 24

y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588

Thus, there are 13382588 bacteria in 1 day

<em><u>Determine how many will be in 1 week</u></em>

1 week = 168

Substitute t = 168

y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}

Thus there are 10(1.8)^{168} bacteria in 1 week

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