This is the theory of exponential growth. Given that the an athlete is training to run marathon and she plans to run 2 miles in the first week and increase the distance by 8%. The function modeling how far she will run the nth week will be given by
nth=ae^(bx)
nth=2e^(0.08x)
where x is the nth time.
Answer: B. Distributive Property
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The area of a triangle is given by:
![A=\frac{1}{2} bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20bh)
The base is 14 and the height is 8. Plug it into the formula:
![A=\frac{1}{2} (8)(14)\\A=4(14)\\A=56\text{ cm}^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%288%29%2814%29%5C%5CA%3D4%2814%29%5C%5CA%3D56%5Ctext%7B%20cm%7D%5E2)
Answer:
324
Step-by-step explanation:
Given:
![g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt](https://tex.z-dn.net/?f=g%28x%29%3D4x%5E2%2B2x%5C%5C%20%5C%5Cf%28x%29%3D%5Cint%5Climits%5Ex_0%20%7Bg%28t%29%7D%20%5C%2C%20dt)
Find:
![f(6)](https://tex.z-dn.net/?f=f%286%29)
First, find f(x):
![f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2](https://tex.z-dn.net/?f=f%28x%29%5C%5C%20%5C%5C%3D%5Cint%5Climits%5Ex_0%20%7Bg%28t%29%7D%20%5C%2C%20dt%5C%5C%20%5C%5C%3D%5Cint%5Climits%5Ex_0%20%7B%284t%5E2%2B2t%29%7D%20%5C%2C%20dt%5C%5C%20%5C%5C%3D%5Cleft%284%5Ccdot%20%5Cdfrac%7Bt%5E3%7D%7B3%7D%2B2%5Ccdot%20%5Cdfrac%7Bt%5E2%7D%7B2%7D%5Cright%29%5Cbig%7C%5Climits%5Ex_0%5C%5C%20%5C%5C%3D%5Cleft%28%5Cdfrac%7B4t%5E3%7D%7B3%7D%2Bt%5E2%5Cright%29%5Cbig%7C%5Climits%5Ex_0%5C%5C%20%5C%5C%3D%20%5Cleft%28%5Cdfrac%7B4x%5E3%7D%7B3%7D%2Bx%5E2%5Cright%29-%5Cleft%28%5Cdfrac%7B4%5Ccdot%200%5E3%7D%7B3%7D%2B0%5E2%5Cright%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B4x%5E3%7D%7B3%7D%2Bx%5E2)
Now,
![f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324](https://tex.z-dn.net/?f=f%286%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B4%5Ccdot%206%5E3%7D%7B3%7D%2B6%5E2%5C%5C%20%5C%5C%3D288%2B36%5C%5C%20%5C%5C%3D324)
Answer:which z sqore are u talking about
Step-by-step explanation: