Answer:
[tex]f(x)=10,000(1.05)^{x}[/tex]
Step-by-step explanation:
The exponential regression form is :
y = a(b)^x
∵ x = 0 ⇒ y = 10,000
∴ 10,000 = a(b)^0 ⇒ 10,000 = a(1) where b^0 = 1
∴ a = 10,000
∵ x = 10 ⇒ y = 16,000
∴ 16,000 = 10,000(b)^10
∴ [tex]b^{10}[/tex] = 16,000 ÷ 10,000 = 1.6
∴ [tex]b=(1.6)^{\frac{1}{10}}[/tex] = 1.048 ≅ 1.05 (to the nearest hundredth)
∴ [tex]y=10,000(1.05)^{x}[/tex]
