Question

3) Seja uma função exponencial f(x) = k.a x tal que f(3) = 18 e f(5) = 648. Determine o valor de k -1 .

Answer 1

$\Large\boxed{\begin{array}{l}\sf f(x)=k\cdot a^x\\\sf f(3)=k\cdot a^3\\\sf k\cdot a^3=18.\\\sf f(5)=k\cdot a^5\\\sf k\cdot a^5=648\\\sf\dfrac{\diagup\!\!\!k\cdot a^5}{\diagup\!\!\!k\cdot a^3}=\dfrac{648}{18}\\\\\sf a^2=36\\\sf a=\sqrt{36}\\\sf a=6\\\sf f(3)=k\cdot a^3\\\sf 18=k\cdot 6^3\\\sf 216k=18\\\sf k=\dfrac{18\div18}{216\div18}=\dfrac{1}{12}\\\\\sf k-1=\dfrac{1}{12}-1=\dfrac{1-12}{12}\\\huge\boxed{\boxed{\boxed{\boxed{\sf k-1=-\dfrac{11}{12}}}}}\end{array}}$