Question

Write an exponential function y= ab^x for a graph that includes (1,15) and (0,6)

Answer 1

basically you write an exponential function for y=ab^x for a graph that includes (1,15) and (0,6)
then using (0,6) you get: 6 = ab^0 
and using (1,15) you get 15 = ab^1

Equations:
a = 6
ab = 15
So, b = 15/6 = 5/2
Equation:
y = 6(5/2)^x

Answer 2

Answer:

The required exponential function is $y=6(\frac{5}{2})^x$.

Step-by-step explanation:

The general exponential function is

$y=ab^x$

It is given that graph includes (1,15) and (0,6). It means the equation must be satisfied by these points.

$15=ab^1$              .... (1)

$6=ab^0$

$6=a$

The value of a is 6. Put this value in equation (1).

$15=(6)b$

Divide both sides by 6.

$\frac{15}{6}=b$

$\frac{5}{2}=b$

The value of b is $\frac{5}{2}$.

Put a=6 and $b=\frac{5}{2}$ in the general exponential function.

$y=6(\frac{5}{2})^x$

Therefore the required exponential function is $y=6(\frac{5}{2})^x$.