Isabella has a dozen apples of the same size and a dozen

The population of a small town was 3500 in 2005. The population increases by 4% annually. A. Write an exponential growth functio

nika2105 [10]

Answer: The population in 2025 will be 7669

Step-by-step explanation:

a) When we have an initial quantity A, and we have an increase of the X%, the new quantity is written as:

new quantity = A + A*(X%/100%) = A*(1 + X%/100%)

In this case, our initial quantity is 3500, the town's population in 2005.

And X% = 4%.

We know that each year, the population increases by 4%.

Then if P(1) is the population one year after 2005, this is:

P(1) = 3500*(1 + 4%/100%) = 3500*(1.04)

After another year, the population increases again:

P(2) = (3500*(1.04))*(1 + 4%/100%)) = 3500*(1.04)*(1.04) = 3500*(1.04)^2

Well, we already can see the pattern here, the population N years after 2005 will be:

P(N) = 3500*(1.04)^N

b) Now we want to know the population in 2025.

N represents the number of years after 2005, then we will have:

N = 2025 - 2005 = 20

2025 is 20 years after 2005.

Then the population in 2025 will be:

P(20) = 3500*(1.04)^20 = 7,668.9

And we can not have a 0.9 of a person, so we should round it up to the next whole number, then the population in 2025 will be 7669

5 0

3 years ago

Find the area of the triangle that has a base of 16 yd and a height of 9 yd.

kherson [118]

Area=1/2Bh
Area=1/2(16)(9)
Area=(8)(9)
Area=72yd

7 0

3 years ago

Express y = -2x² - 4x + 7 in the form of perfect square and find the maximum points.

Marat540 [252]

Answer:

<em>Maximum: (-1,9)</em>

Step-by-step explanation:

<u>Vertex form of the quadratic function</u>

If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:

$y=a(x-h)^2+k$

Where a is the leading coefficient.

We are given the following function:

$y =-2x^2-4x+7$

To find the vertex, we need to complete squares. First, factor -2 on the first two terms:

$y =-2(x^2+2x)+7$

The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:

$y =-2(x^2+2x+1- 1)+7$

Taking out the -1:

$y =-2(x^2+2x+1)+2+7$

Factoring the trinomial and operating:

$y =-2(x+1)^2+9$

Comparing with the vertex form we have

Vertex (-1,9)

Leading coefficient: -2

Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.

Maximum: (-1,9)

3 0

2 years ago

Anna and Carla are 9 miles apart on a path when they start moving toward each other. Anna runs at a constant speed of 4 miles pe

Sergio [31]

Answer:

The answer is 3 miles.

4+2=6 , 6-9=3

4 0

3 years ago

An ant travels at a constant rate of 30 cm every 2 minutes at what pace does the ant travel per centimeter

Rama09 [41]

Answer:

Answer: 15 cm in one minute. Step-by-step explanation: If the ant travels at 30 cm every two minutes, then divide both numbers by two to get the unit rate, which is 15 I'm per minute

6 0

3 years ago