Okay, the exponential function is
![g = a^{x}](https://tex.z-dn.net/?f=g%20%3D%20a%5E%7Bx%7D%20)
The start price of it in t=0 is 3,500, as we can see on the graph. Then, the function becomes
![g = 3500^{x}](https://tex.z-dn.net/?f=g%20%3D%203500%5E%7Bx%7D%20)
Let's see at t=2, where the price is g=2000:
![2000 = 3500^{x}](https://tex.z-dn.net/?f=2000%20%3D%20%203500%5E%7Bx%7D%20)
Take natural logarithm:
![ln 2000 = ln 3500^{x}](https://tex.z-dn.net/?f=ln%202000%20%3D%20ln%20%203500%5E%7Bx%7D%20)
![x*ln 3500 = ln 2000](https://tex.z-dn.net/?f=x%2Aln%203500%20%3D%20ln%202000)
![x = \frac{ln 2000}{ln 3500} = 0.93](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7Bln%202000%7D%7Bln%203500%7D%20%3D%200.93)
So, the difference between t=0 and t=2 is
![x_{t=0} - x_{t=2} = 1 - 0.93 = 0.07](https://tex.z-dn.net/?f=x_%7Bt%3D0%7D%20%20-%20%20x_%7Bt%3D2%7D%20%20%3D%201%20-%200.93%20%3D%200.07)
And then we get the change of x in one year equal to 0.035.
So, the final equation is
![g = 3500^{1-0.035t}](https://tex.z-dn.net/?f=g%20%3D%20%203500%5E%7B1-0.035t%7D%20)
You can insert any t and see that it is correct, for example t=7
You would use 1.07 for that
Answer:
![\frac{7}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B12%7D%20)
Step-by-step explanation:
![2 \frac{1}{3} - 1 \frac{3}{4}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B3%7D%20%20-%201%20%5Cfrac%7B3%7D%7B4%7D%20)
The fractions above are known as mixed numbers (that is, fractions that contain the combination of a whole number and proper fraction). The mixed numbers can equally be renamed as improper fractions. However, renaming can only occur the the mixed numbers are being transformed as below:
![\frac{7}{3} - \frac{7}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B3%7D%20%20-%20%20%5Cfrac%7B7%7D%7B4%7D)
The transformation occur through a simple approach thus: for the first mixed number; 2 1/3 = 2 multiplied by 3 plus 1 divide by 3 equals 7/3. Similarly, mixed number 1 3/4 is transformed by this: 1 multiplied by 4 plus 3 divide by 4 equals 7/4.
Simplifying further to arrive at final result implies,
![\frac{7}{3} - \frac{7}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B3%7D%20%20-%20%20%5Cfrac%7B7%7D%7B4%7D%20)
Take the LCM of the denominators (4 × 3 =12) and simplify thus:
![= \frac{28 - 21}{12}](https://tex.z-dn.net/?f=%20%3D%20%20%20%5Cfrac%7B28%20-%2021%7D%7B12%7D%20)
![= \frac{7}{12}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B7%7D%7B12%7D%20)
Answer:
D
Step-by-step explanation:
in the question the scale factor is 4 so that means it is a dilation (getting larger) because the scale factor is >1