The two graphs you uploaded represent the functions:

• $y = 5x$ (linear growth) on the left
• $y = 5^x$ (exponential growth) on the right

Let's break down the growth between $x = 0$ and $x = 2$:

1. For $y = 5x$: This is a linear function where the value of $y$ increases by 5 for each unit increase in $x$.

   • At $x = 0$, $y = 0$
   • At $x = 2$, $y = 10$ The growth is constant and predictable.

2. For $y = 5^x$: This is an exponential function, where the value of $y$ increases by multiplying 5 for each unit increase in $x$.

   • At $x = 0$, $y = 5^0 = 1$
   • At $x = 2$, $y = 5^2 = 25$ The growth rate increases more rapidly.

Comparing Growth:

From $x = 0$ to $x = 2$, the exponential function $y = 5^x$ grows faster than the linear function $y = 5x$. This is evident because $y = 5x$ reaches 10 at $x = 2$, whereas $y = 5^x$ reaches 25.

Correct Answer:

• $y = 5x$ grows slower than $y = 5^x$.

Would you like further details or have any questions?

Here are five related questions to extend your understanding:

1. How does the slope of a linear function like $y = 5x$ relate to its growth?
2. What would happen to the exponential growth if the base of the exponent changed from 5 to 2 in $y = 5^x$?
3. Can you determine the point where $y = 5^x$ overtakes $y = 5x$ for larger values of $x$?
4. How does the concept of "exponential growth" apply in real-world scenarios like population growth?
5. How would the graph change if the linear function had a different slope, such as $y = 2x$?

Tip: When comparing functions, always pay attention to whether they exhibit linear, exponential, or logarithmic growth patterns, as these grow at very different rates over time.