<span>Density is a mathematical expression that calculates the mass of the object by its volume:
Data:
m (mass) = 5 grams
v (volume) </span>≈ 0.689 cm³
d (density) = ?
Formula:
![d = \frac{m}{v}](https://tex.z-dn.net/?f=d%20%3D%20%20%5Cfrac%7Bm%7D%7Bv%7D%20)
Solving:
![d = \frac{m}{v}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bm%7D%7Bv%7D%20)
![d = \frac{5}{0.689}](https://tex.z-dn.net/?f=d%20%3D%20%20%5Cfrac%7B5%7D%7B0.689%7D%20)
7+d=19 is the answer
subtract 7 from each side d=19-7
d=12
Answer: 18 years
Work Shown:
![f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\](https://tex.z-dn.net/?f=f%28%5Ctext%7Bx%7D%29%20%3D%202.56%281.04%29%5E%5Ctext%7Bx%7D%5C%5C%5C%5C5%20%3D%202.56%281.04%29%5E%5Ctext%7Bx%7D%5C%5C%5C%5C5%2F2.56%20%3D%20%281.04%29%5E%5Ctext%7Bx%7D%5C%5C%5C%5C1.953125%20%3D%20%281.04%29%5E%5Ctext%7Bx%7D%5C%5C%5C%5C%5Clog%281.953125%29%20%3D%20%5Clog%281.04%5E%5Ctext%7Bx%7D%29%5C%5C%5C%5C%5Clog%281.953125%29%20%3D%20%5Ctext%7Bx%7D%2A%5Clog%281.04%29%5C%5C%5C%5C%5Ctext%7Bx%7D%20%3D%20%5Cfrac%7B%5Clog%281.953125%29%7D%7B%5Clog%281.04%29%7D%5C%5C%5C%5C%5Ctext%7Bx%7D%20%5Capprox%2017.0682937693249%5C%5C%5C%5C)
The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is
so we can pull down the exponent.
From here it seems your teacher wants you to round up to the nearest integer.
If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.
While x = 18 leads to f(x) = 5.19
Therefore, x = 18 has the price reach or exceed $5
Answer:
The last graph
Step-by-step explanation:
The problem presented here is similar to a compound interest problem since we have an initial value, a growth constant and the aspect of time.
We can consider the number of television sets currently produced by the company to be our Principal amount;
P = 2000
The rate of increase in production per month can be considered as our interest rate earned;
r = 25% = 0.25
The total number of television sets y will be our Accumulated amount;
A = y
The duration x becomes our time n.
The compound interest formula is given as;
![A=P(1+r)^{n}](https://tex.z-dn.net/?f=A%3DP%281%2Br%29%5E%7Bn%7D)
We simply substitute the given information into the formula;
![y=2000(1.25)^{x}](https://tex.z-dn.net/?f=y%3D2000%281.25%29%5E%7Bx%7D)
This is an exponential growth function since the base of the exponent x is greater than 1.
A graph of the function will be an exponential curve passing through ( 0, 2000) since 2000 is our initial value