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3 years ago

6

A baseball tournament begins with 128 teams. After each round of games, only half of the teams are left. How many teams will be

left after three rounds of games?

1 answer:

krek1111 [17]3 years ago

8 0

Answer:

End of round 1:

128 ÷ 2 = 64

End of round 2:

64 ÷ 2 = 32

End of round 3:

32 ÷ 2 = 16

Step-by-step explanation:

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Drupady [299]

Let f=number of flowers in a vase, then:

5f-16=24 add 16 to both sides

5f=40 divide both sides by 5

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Answer:

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Finger [1]

Solution

a)

To find the exponential growth function, we apply the exponential growth formula which is

$N(t)=a(1+k)^t$

Where

$\begin{gathered} a\text{ is the }initial\text{ population} \\ k\text{ is the growth rate} \\ t\text{ is the number of time intervals} \end{gathered}$

Given that

$\begin{gathered} a=23,900 \\ N(5)=25,100 \\ t=2012-2007=5 \end{gathered}$

Substitute the variables into the exponential growth formula

$\begin{gathered} 25100=23900(1+k)^5 \\ \text{Divide both sides by 23,900} \\ \frac{25100}{23900}=\frac{23900(1+k)^5}{23900} \\ 1.05021=(1+k)^5^{} \\ \sqrt[5]{1.05021}=1+k \\ 1.00984=1+k \\ \text{Collect like terms} \\ k=1.00984-1 \\ k=0.00984 \end{gathered}$

Hence, the exponential growth function is

$\begin{gathered} N(t)=23900(1+0.00984)^t_{} \\ N(t)=23900(1.00984)^t \end{gathered}$

Hence, the exponential growth function is

$N(t)=23900(1.00984)^t$

b)

For the population of the city in 2022,

$\begin{gathered} t=2022-2007=15 \\ t=15 \end{gathered}$

Substitute for t into the exponential growth function

$\begin{gathered} N(t)=23900(1.00984)^t \\ N(15)=23900(1.00984)^{15} \\ N(15)=27700\text{ (nearest hundred)} \end{gathered}$

Hence, the population is 2022 is 27700 (nearest hundred)

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