Final answer:
To find an exponential function y = abˣ that passes through (0,15) and (2,1215), we set a to 15 (since any number to the power of 0 is 1), and then solve for b using the second point to find b = 9. The resulting function is y = 15*9ˣ.
Step-by-step explanation:
To write an exponential function in the form y = ab⁴ that goes through the points (0,15) and (2,1215), we need to determine the values of ‘a’ and ‘b’. The first point (0,15) tells us that when x=0, y=15. According to our function form y = ab⁴, if we substitute x=0, we get y = a*b⁰, which simplifies to y = a, since any number to the power of 0 is 1. Therefore, a = 15.
Using the second point (2,1215), we substitute x=2 into the equation to get 1215 = 15*b². To find the value of b, we divide both sides by 15, which gives us b² = 1215/15, hence b² = 81. Now we can take the square root of both sides to get b = 9 (‘b’ is positive since it's a growth factor).
The final exponential function is y = 15*9⁴.