Question

If f(x) is an exponential function where f(-1.5) 26 and

Answer 1

Answer:

$f(10) = 1147.25$

Step-by-step explanation:

Given

$f(-1.5) = 26$

$f(5.5) = 7$

Required

f(10)

An exponential function is represented as:

$f(x) = ab^x$

$f(-1.5) = 26$ impleies that:

$26 = ab^{-1.5}$ --- (1)

$f(5.5) = 7$ implies that

$7 = ab^{5.5}$ --- (2)

Divide (2) by (1)

$26/7 = ab^{-1.5}/ab^{5.5}$

$3.71429 = b^{-1.5+5.5}$

$3.71429 = b^{4}$

Take 4th root

$b = 1.39$

Substitute $b = 1.39$ in $26 = ab^{-1.5}$

$26 = a * 1.39^{-1.5}$

$26 = a * 0.6102$

Solve for (a)

$a = 26/0.6102$

$a = 42.61$

f(10) is calculated as:

$f(10) = ab^{10}$

$f(10) = 42.61 * 1.39^{10}$

$f(10) = 1147.25$