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musickatia [10]
3 years ago
8

The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less t

han 12,000?
Mathematics
1 answer:
just olya [345]3 years ago
3 0

This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

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Members of the Wide Waters Club pay
vivado [14]

Answer:

The number of times members and non-members will have to rent a boat in order to pay the same amount=20

Step-by-step explanation:

We can have two expressions to show the total cost paid by a member and non-member;

Total cost by member=Cost per summer season+cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per summer season=$105

Cost per number of times they rent a boat=$9.50

Number of times they rent a boat=n

Replacing;

Total cost by a member=105+(9.5×n)=9.5 n+105......equation 1

Total cost by a non-member=Cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per number of times they rent a boat=$14.75

Number of times they rent a boat=n

Replacing;

Total cost by a non-member=(14.75×n)=14.75 n......equation 2

To calculate the number of times they would have to rent a boat in order to pay the same amount, we equate equation 1 to equation 2

9.5 n+105=14.75 n

14.75 n-9.5 n=105

5.25 n=105

n=105/5.25

n=20

The number of times members and non-members will have to rent a boat in order to pay the same amount=20

6 0
3 years ago
Circle O is inscribed in square EFGH.
Citrus2011 [14]

Answer:

D) 25.5 cm

Step-by-step explanation:

Circumference = pi × d

20 = 3.14 × d

d = 6.3694267516

Diameter = length of one side

Perimeter of the square = 4s

4(6.3694267516)

25.4777070064 cm

From the options, closest is 25.5

3 0
3 years ago
What is 32.043 in expanded form?
SashulF [63]
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7 0
3 years ago
A Rhombus with diagonal 1 equal to 5 ft and diagonal 2 equal to 8 ft
Minchanka [31]

Answer:

Area = 20 ft²

Step-by-step explanation:

Area of a thrombus

½ × d1 × d2

½ × 5 × 8

20

4 0
3 years ago
Read 2 more answers
If angle A = 34°, angle B = (x-5)°, angle C = 4y °, what is the value of y?
nevsk [136]
180-34=146
146-5=141
ratio=1:4
1+4=5
141÷5=28.2
x=28.2
y=112.8

I may be wrong, ask for more opinions
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--- O
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4 0
3 years ago
Read 2 more answers
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