Question

Write the equation for an exponential function, in the form y=a x b^x, whose graph though the coordinate points (1,7.5) and (3,16.875).

Answer 1

Answer: y = 5(1.5)ˣ is your answer

Answer 2

y = 5*(1.5)ˣ

Explanation:

The exponential function is given in the form y = a*bˣ.

Given coordinate points are (1, 7.5) and (3, 16.875).

It means 7.5 = a*b¹ and 16.875 = a*b³

Dividing the second equation by the first equation:-

16.875 / 7.5 = a*b³ / a*b¹

b² = 2.25

b = 1.5

Now substitute the value of b into first equation:-

7.5 = a*1.5

a = 7.5/1.5

a = 5

Hence, y = 5*(1.5)ˣ