SMARTPHONE A new smartphone application is available for download. The number $$ y $$ of downloads can be modeled by the function $$ y=6.3 x^{2}+3000 $$, where $$ x $$ is the number of hours since the new application was released. How many hours does it take for the number of downloads to reach 3630 ? (Section 8.3)

Question

UpStudy AI · Accepted Answer

To determine how many hours it takes for the number of downloads $$ y $$ to reach **3630**, given the model:

$$
y = 6.3x^{2} + 3000
$$

where $$ x $$ is the number of hours since the application was released, follow these steps:

### Step 1: Set Up the Equation

Set the number of downloads $$ y $$ to **3630** and substitute into the equation:

$$
3630 = 6.3x^{2} + 3000
$$

### Step 2: Isolate the Quadratic Term

Subtract **3000** from both sides to isolate the quadratic term:

$$
3630 - 3000 = 6.3x^{2}
$$

$$
630 = 6.3x^{2}
$$

### Step 3: Solve for $$ x^{2} $$

Divide both sides by **6.3** to solve for $$ x^{2} $$:

$$
x^{2} = \frac{630}{6.3}
$$

$$
x^{2} = 100
$$

### Step 4: Take the Square Root

Take the square root of both sides to solve for $$ x $$:

$$
x = \sqrt{100}
$$

$$
x = 10
$$

### Conclusion

It takes **10 hours** for the number of downloads to reach **3630**.
It takes 10 hours for the number of downloads to reach 3630.

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions