Question

Write the equation for an exponential form, in the form y=axb^x, whose graph passes through the coordinate points (1, 7.5) and (3, 16.875).

Answer 1

The exponential function is :
y=ab^x
We have two points:
(1, 7.5)
(3, 16.875)

First point:
(1 , 7.5)
x=1
y=7.5

y=ab^x
7.5=ab¹

Second point:
(3 , 16.875)
x=3
y=16.875

y=ab^x
16.875=ab³

Then, always is true that.

7.5 / 16.875 = (ab) / (ab³)

7.5(ab³)=16.875(ab)
7.5ab³ / a
b²=16.875
7.5b²=16.875
b=⁺₋√(16.875 / 7.5)
b=⁺₋1.5

if b=-1.5 ⇒ 7.5=a(-1.5) ⇒a=-5
y=-5*(-1.5)^x
y=5(1.5^x)

if b=1.5 ⇒ 7.5=a(1.5) ⇒ a=5
y=5*(1.5^x)

Answer; y=5*1.5^x