Answer: 9 in
Step-by-step explanation:
Answer:
D one real solution
Step-by-step explanation:
x^2 - 8x + 16 = 0
This is in the form
ax^2 +bx + c = 0
so we can use the discriminant to determine the number of solutions
b^2 -4ac
(-8)^2 -4(1)(16)
64 - 64
0
Since the discriminant is zero, there is one real solution.
Answer:
so rate is 4.72 %
Step-by-step explanation:
Given data
time (t) = 5 year = 5×4 = 20 quarterly
amount = $27456
principal = $1225
to find out
interest rate (r)
solution
we use here amount formula that is
amount = principal (
-1 ) / r .....................1
put all value principal , amount and time in equation 1 and we get rate
rate is r/4 because it is quarterly payment
amount = principal (
-1 ) / r/4
27456 = 1225 (
-1 ) / r/4
(
-1 ) / r/4 = 27456/ 1225
(
-1 ) / r = 27456/ (1225 × 4)
(
-1 ) = r 27456/ (1225 × 4)
now by the tvm solver and amount $27456
graph value
we get r = 0.0472
so rate is 4.72 %
Answer:
They'll reach the same population in approximately 113.24 years.
Step-by-step explanation:
Since both population grows at an exponential rate, then their population over the years can be found as:
![\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%7D%28t%29%20%3D%20%5Ctext%7Bpopulation%7D%280%29%2A%281%20%2B%20%5Cfrac%7Br%7D%7B100%7D%29%5Et)
For the city of Anvil:
![\text{population anvil}(t) = 21000*(1.04)^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20anvil%7D%28t%29%20%3D%2021000%2A%281.04%29%5Et)
For the city of Brinker:
![\text{population brinker}(t) = 7000*(1.05)^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20brinker%7D%28t%29%20%3D%207000%2A%281.05%29%5Et)
We need to find the value of "t" that satisfies:
![\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20brinker%7D%28t%29%20%3D%20%5Ctext%7Bpopulation%20anvil%7D%28t%29%5C%5C21000%2A%281.04%29%5Et%20%3D%207000%2A%281.05%29%5Et%5C%5Cln%5B21000%2A%281.04%29%5Et%5D%20%3D%20ln%5B7000%2A%281.05%29%5Et%5D%5C%5Cln%2821000%29%20%2B%20t%2Aln%281.04%29%20%3D%20ln%287000%29%20%2B%20t%2Aln%281.05%29%5C%5C9.952%20%2B%20t%2A0.039%20%3D%208.8536%20%2B%20t%2A0.0487%5C%5Ct%2A0.0487%20-%20t%2A0.039%20%3D%209.952%20-%208.8536%5C%5Ct%2A0.0097%20%3D%201.0984%5C%5Ct%20%3D%20%5Cfrac%7B1.0984%7D%7B0.0097%7D%5C%5Ct%20%3D%20113.24)
They'll reach the same population in approximately 113.24 years.