Question

Find the equation for the exponential function f (x) = b .aˣ that passes through the points (0,6) and (1,11).

Answer 1

Answer:

$f(x)=6.(1,83)^{x}$

Step-by-step explanation:

We have two points (0,6) and (1,11) and to find the exponential function that passes through that points we have to substitute them in the equation $f(x)=b.a^{x}$.

Observation: f(x)=y then $y=b.a^{x}$

First we are going to replace the point (0,6) in the equation, where x=0 and y=6.

$y=b.a^{x}\\ 6=b.a^{0}$

Remember: $a^{0}=1$

$6=b.a^{0} \\6=b$

We got the value of b and it's 6. The equation now is:

$y=6.a^{x}$

Finally we have to replace the point (1,11),

$y=6.a^{x} \\ 11=6.a^{1} \\ 11=6.a$

Remember: $a^{1}=a$

Isolating the variable a:

$11=6.a\\ \frac{11}{6} =a\\1,83=a$

We have then, a=1.83 and b=6. Replacing a and b in $f(x)=b.a^{x}$

We obtain:

$f(x)=6.(1,83)^{x}$