Answer:
a = 4000, b = 0.9
Step-by-step explanation:
The standard form of an exponential function is
y = a[tex]b^{x}[/tex]
To find a and b substitute the given points into the equation
Using (0, 4000), then
4000 = a[tex]b^{0}[/tex] = 4000 × 1 = 4000
Hence a = 4000, thus
y = 4000[tex]b^{x}[/tex]
Using (3, 2916), then
2916 = 4000[tex]b^{3}[/tex] (divide both sides by 4000 )
0.729 = [tex]b^{3}[/tex] ( take the cube root of both sides ), thus
b = [tex]\sqrt[3]{0.729}[/tex] = 0.9
