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3 years ago

Find the 7th term of the geometric sequence -5, 15, 45, 135, 405,...

Mathematics

1 answer:

katovenus [111]3 years ago

7 0

Answer:

1,215

Step-by-step explanation:

Because if you think of it it multiplies by 3x so 3x5=? 15! 15x3=? 45! 45x3=? 405! 405x=3? 1,215! 1,215x3=? 3,645! anyways, I can go on and on I hope this answer was right!

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The domain of the function is given. Find the range.

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In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per

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Answer:

The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

Initial population is, $P_0=450,000$

Growth rate is, $r=5\%=0.05$

Final population is, $P=700,000$

A population growth is an exponential growth and is modeled by the following function:

$P=P_0(1+r)^x$

Taking log on both sides, we get:

$\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}$

Plug in all the given values and solve for 'x'.

$x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10$

So, for $x > 9.13$ , the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

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3 years ago