Question

The graph of an exponential function passes through (1, 10) and (4, 80). Find the function that describes the graph.

Answer 1

Answer:

• y = 5*2ˣ

Step-by-step explanation:

Exponential function:

• y = abˣ

Ordered pairs given:

• (1, 10) and (4, 80)

Substitute x and y values to get below system:

• 10 = ab
• 80 = ab⁴

Divide the second equation by the first one and solve for b:

• 80/10 = b³
• b³ = 8
• b = ∛8
• b = 2

Use the first equation and find the value of a:

• 10 = a*2
• a = 5

The function is:

• y = 5*2ˣ

Answer 2

Answer:

$y=5 \cdot 2^x$

Step-by-step explanation:

An exponential function is written in the form:

• $y=ab^x$

We can use the given points that the exponential function passes through to solve for a and b.

Create a system of equations by substituting (1, 10) and (4, 80) into the exponential form of a function.

• $\text{I}:\ 10=ab^1$
• $\text{II}: \ 8 0=ab^4$

Divide Equation I by Equation II in order to cancel out variable a.

• $\displaystyle \frac{80=ab^4}{10=ab}$
• $8=b^3$
• $b=2$

Now we can solve for a by substituting b back into either equation from the system of equations.

• $10=ab$
• $10=a(2)$
• $a=5$

Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).

• $y=5 \cdot 2^x$

y = 5 · 2ˣ is the exponential function that describes the graph.