Question

For the following exercises, find a formula for an exponential function that passes through the two points given. (0,6) and (3,750)

Answer 1

$\boxed{\boxed{f(x)=6(5)^x}}$

Explanation:

An exponential function is given by the following form:

$y=ab^x \\ \\ Where: \\ \\ a \ is \ a \ constant \ and \ b \ is \ the \ base$

Here we know two points:

$(0,6) \ and \ (3,750)$

$\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}$

Finally, our exponential function is:

$\boxed{\boxed{f(x)=6(5)^x}}$

Learn more:

Behavior of functions: https://brainly.com/question/12891789

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