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Tasya [4]
4 years ago
8

A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential

growth formula. Round your answer to the nearest million.
Mathematics
1 answer:
aliina [53]4 years ago
6 0
Let t=number of years since 1991.
Then 
P(t)=147 e^(kt)   ... in millions
P(0)=147 e^(0)=147
P(7)=147 e^(7k)=153
e^(7k)=(153/147)
take ln both sides
ln(e^(7k))=ln(153/147)
7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26
P(26)=147e^(26*.005715)=170.55
Answer: in 2017, the projected population is 170.55 millions.
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A carpenter added a diagonal brace to gate. The gate is 8ft. Wide and 10 ft. Tall. How long is the brace
jeyben [28]

Answer:

The brace is 2\sqrt{41} ft ≅ 12.806 ft long

Step-by-step explanation:

The length of the diagonal of a rectangle can be found using this rule

d=\sqrt{l^{2}+w^{2}} , where

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  • w is its width

∵ The gate has shaped a rectangle

∵ Its length = 10 ft

∵ Its width = 8 ft

∴ l = 10 and w = 8

∵ The brace is the diagonal

→ By using the rule above

∴ d=\sqrt{(10)^{2}+(8)^{2}}=\sqrt{100+64}=\sqrt{164}

∴ The length of the brace = 2\sqrt{41} ≅ 12.806 ft

∴ The brace is 2\sqrt{41} ≅ 12.806 ft long

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