anonymous
  • anonymous
HELP?!
Mathematics
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

mathstudent55
  • mathstudent55
How do you show growth?
mathstudent55
  • mathstudent55
For example, if the growth is a certain percentage each year, what equation shows growth?
mathstudent55
  • mathstudent55
Let's say the growth is 10%. Since 100% + 10% = 110% = 1.1, then each year, multiply the previous year's amount by 1.1 Year 0 a Year 1 1.1a Year 2 1.1(1.1a) = 1.1^2 * a Year 3 1.1(1.1^2)a) = 1.1^3 * a Year x 1.1^x * a

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathstudent55
  • mathstudent55
In your case, the growth is 20%, so we use 1.2 Neighborhood A \(y = 30 \times 1.2^x\)
anonymous
  • anonymous
and I would just replace x with 5?
mathstudent55
  • mathstudent55
In Neighborhood B, you start with 45 and the growth is linear, so its: Year 0 45 houses Year 1 45 + 3 * 1 Year 2 45 + 3 * 2 Year 4 45 + 3 * 3 etc. Year x 45 + 3 * x \(y = 45 + 3x\)
mathstudent55
  • mathstudent55
Part A. Neighborhood A. \(y = 30 \times 1.2^x\) Neighborhood B. \(y = 45 + 3x\)
mathstudent55
  • mathstudent55
Part B. Let x equal 5 in each of the two functions above to find the number of homes in the two neighborhoods after 5 years.
mathstudent55
  • mathstudent55
Part C. Set the two functions equal and solve for x.
anonymous
  • anonymous
so y=30*1.2^5 and y=45+3(5) for B?
mathstudent55
  • mathstudent55
Yes, and evaluate each expression.
anonymous
  • anonymous
y=74.6496 y=60
mathstudent55
  • mathstudent55
Good. 75 & 60
mathstudent55
  • mathstudent55
Notice that Neighborhood A started with 30 homes and B with 45. By year 5, Neighborhood A already has more homes than B. This gives you a hint as to the solution of part C.
anonymous
  • anonymous
what would I set my function equal to?
anonymous
  • anonymous
would I make a function table and use the formula until I get the same number of houses?
mathstudent55
  • mathstudent55
For Part C?
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
\(30 \times 1.2^x = 45 + 3x\)
anonymous
  • anonymous
ohhh ok... and so that's all I need for part c, is to solve that?
mathstudent55
  • mathstudent55
You can use a table. The hint I mentioned above is that since by year 5, Neighborhood A already has more homes than Neighborhood B, that means the year they have the same number of homes is between years 0 and 5.
mathstudent55
  • mathstudent55
Yes, up need to solve the equation, but your idea of letting x = 1, 2, 3, 4, 5 is good.
mathstudent55
  • mathstudent55
Make a table and see when Neighborhood A overtakes B.
anonymous
  • anonymous
awee yes I get it now
mathstudent55
  • mathstudent55
Are you given choices?
anonymous
  • anonymous
no it's open response
anonymous
  • anonymous
I'm making a table rn
mathstudent55
  • mathstudent55
OK. Then do what you mentioned above. Make a table.
mathstudent55
  • mathstudent55
We already know this: |dw:1438567229776:dw|
mathstudent55
  • mathstudent55
It happens between year 3 and year 4. |dw:1438567359681:dw|
anonymous
  • anonymous
ok thanks for that because I was plugging in the different numbers and didn't see when they were equal, I didn't know that it could be in between years. So it would be after approximately 3 and a half yrs?
mathstudent55
  • mathstudent55
The smallest difference between A and B is at 3.3 years, so that is a close approximation. |dw:1438567705900:dw|
mathstudent55
  • mathstudent55
Your guess of approximately 3.5 years is also good.
anonymous
  • anonymous
Oh my gosh! You were more than helpful and I honestly understand and appreciate everything you've told me. Thank you sooooo much!!! If I were there I'd give you a hug! Absolute lifesaver!!!
mathstudent55
  • mathstudent55
You are very welcome. I just want to mention one point. I don't know if you've learned logarithms yet. Usually, when you have an equation with a variable in the exponent, you use logarithms to find the solution. In this case, the equation we had does not lend itself to taking logarithms of both sides and simplifying easily. That is why I recommended you use a table with values (which was your idea) to see when the functions are of equal value to then see at which time the number of homes are the same.
anonymous
  • anonymous
You are correct, I have not learned logarithms yet, but I will remember your advice.

Looking for something else?

Not the answer you are looking for? Search for more explanations.