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Diano4ka-milaya [45]
3 years ago
15

Find the value of x. 2(x-3)-17=13-3(x+2)

Mathematics
2 answers:
Nonamiya [84]3 years ago
5 0
Solve your equation step-by-step.

2(x−3)−17=13−3(x+2)

Simplify both sides of the equation.

2(x−3)−17=13−3(x+2)

Simplify

2x−23=−3x+7

Add 3x to both sides.

2x−23+3x=−3x+7+3x

5x−23=7

Add 23 to both sides.

5x−23+23=7+23

5x=30

Divide both sides by 5.

5x/5 = 30/5

x=6

nordsb [41]3 years ago
5 0
Expanding, we have:
2x-23=7-3x
Adding 3x+23 to both sides, we have:
5x=30

Dividing by 5, therefore, x=6.
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In​ 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87​% per year. ​a) Find the exponential g
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Answer:

a) The exponential growth function

P(t) = 5,690,000(1.0287)^t

b) 6,742,868.7374 million

c) 12.04 years

d) 2439.0243902

Step-by-step explanation:

In​ 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87​% per year. ​

The formula for exponential growth is given as:

P(t) = Po( 1 + r) ^t

Where P = Population size after time t

Po = Initial population size

r = Growth rate in percentage

t= time in years

a) Find the exponential growth function.

P(t) = Population size after time t

Po = Initial population size = 5.69 million

r = Growth rate in percentage = 2.87% = 0.0287

t= time in years

The Exponential growth function

P(t) = 5,690,000(1 + 0.0287)^t

P(t) = 5,690,000(1.0287)^t

​b) Estimate the population of the city in 2018. ​

From 2012 to 2018 = 6 years

t = 6 years

Hence,

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^6

P(t) = 5,690,000(1.0287)^6

P(t) = 6,742,868.7374 million

c) When will the population of the city be ​8 million?

P(t) = 8,000,000

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1.0287)^t

Divide both sides by 5,690,000

8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000

= 1.4059753954 = 1.0287^t

Take logarithm of both sides

log 1.4059753954 = log 1.0287^t

Log 1.4059753954 =t Log 1.0287

t = Log 1.4059753954/Log 1.0287

t = 12.041740264

t = 12.04 years

​d) Find the doubling time.

The formula is given as 70/Growth rate

= 70/0.0287

= 2439.0243902

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