Number 1 is answer 1 Number 2 is answer 3 Number 3 is answer 4
Answer:
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Step-by-step explanation:
Given
---x = 0, in 2012
-- x = 5, in 2017
Required
Select all possible equations
Because there is a reduction in the population, as time increases; the rate must be less than 1.
An exponential function is represented as:
![f(x) = ab^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ab%5Ex)
Where
![b = rate](https://tex.z-dn.net/?f=b%20%3D%20rate)
rate > 1 in options (a) and (b) i.e. 1.03
This implies that (a) and (b) cannot be true
For option (c), we have:
![f(x) = 63000(0.97)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2063000%280.97%29%5Ex)
Set x = 0
![f(0) = 63000(0.97)^0 = 63000*1=63000\\](https://tex.z-dn.net/?f=f%280%29%20%3D%2063000%280.97%29%5E0%20%3D%2063000%2A1%3D63000%5C%5C)
Set x = 5
![f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100](https://tex.z-dn.net/?f=f%285%29%20%3D%2063000%280.97%29%5E5%20%3D%2063000%2A0.8587%3D54098.1%20%5Capprox%2054100)
<em>This is true because the calculated values of f(0) and f(5) correspond to the given values</em>
For option (d), we have:
![f(x) = 52477(0.97)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2052477%280.97%29%5Ex)
Set x = 0
![f(0) = 52477(0.97)^0 - 52477* 1 = 52477](https://tex.z-dn.net/?f=f%280%29%20%3D%2052477%280.97%29%5E0%20-%2052477%2A%201%20%3D%2052477)
<em>This is false because the calculated value of f(0) does not correspond to the given value</em>
For option (e), we have:
![f(x) = 63000(0.97)^\frac{1}{5x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%2063000%280.97%29%5E%5Cfrac%7B1%7D%7B5x%7D)
Set x = 0
undefined
<em>This is false because the f(x) is not undefined at x = 0</em>
For option (f), we have:
![f(x) = 52477(0.97)^{5x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2052477%280.97%29%5E%7B5x)
Set x = 0
![f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477](https://tex.z-dn.net/?f=f%280%29%20%3D%2052477%280.97%29%5E%7B5%2A0%7D%20%3D%2052477%280.97%29%5E0%20%3D52477%2A1%3D%2052477)
<em>This is false because the calculated value of f(0) does not correspond to the given value</em>
<em>From the computations above, only (c) </em>
<em> is true</em>
Answer:
Step-by-step explanation:
3b⁵ + 15b⁴ - 18b⁷ = 3b⁵ + [3*5*b⁴] - [6*3*b⁷]
=3b⁴*( b + 5 - 6b³)
Answer:
Step-by-step explanation:
A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)
We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday
A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.
The confidence interval of proportions is given by:
π ± z √(π (1-π) /n)
π is the sample proportion.
z is the critical value.
n is the sample size.
For 99% confidence interval the value of z is 2.58
π = 321/650
The confidence interval is given by
=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)
= (0.493846 ± 0.050594)
=(0.4434 , 0.5443)
=(44.34 % , 54.43 %)
Hence a 99% confidence interval for the population mean of high school students that take the bus to school every day is ci=(44.34%, 54.43%)
<u>Learn more about confidence interval:</u>
brainly.com/question/28052710
# SPJ4