Question

if you answer this question i need an explanation so i can do the other questions on my own.write an exponential function whose graph passes through the given points.(0, 3) and (3, 375)

Answer 1

hello

to solve this problem, we have to take individual point and test it with standard equation of an exponential

`y=ae^(\alpha x)`

now we work with the first point which is (0, 3)

put y = 3 and x = 0 in the equation

`\begin{gathered} y=ae^(\alpha x) \\ 3=ae^(\alpha(0)) \\ 3=a\cdot1 \\ a=3 \end{gathered}`

now we know a = 3

we can test the second point which is (3, 375)

x = 3, y = 375 and a = 3

`\begin{gathered} y=ae^(\alpha x) \\ 375=3ae^(\alpha(3)) \\ \text{divide both sides by 3} \\ 125=e^(3\alpha) \\ \text{now we take the natural log of both sides} \\ In(125)=3\alpha \\ 3In5=3\alpha \\ \text{divide both sides by 3} \\ (3In5)/(3)=(3\alpha)/(3) \\ \alpha=In5 \end{gathered}`

now we can rewrite the equation of exponential function

`y=3ae^(In(5)(x))`

we can go ahead to plot the graph now