if ( f(x) ) is an exponential function of the form ( y = ab^{x} ) where ( f(-4.5)=21 ) and ( f(0.5)=82 )…

if ( f(x) ) is an exponential function of the form ( y = ab^{x} ) where ( f(-4.5)=21 ) and ( f(0.5)=82 ), then find the value of ( f(-2) ), to the nearest tenth.

if ( f(x) ) is an exponential function of the form ( y = ab^{x} ) where ( f(-4.5)=21 ) and ( f(0.5)=82 ), then find the value of ( f(-2) ), to the nearest tenth.

Answer

(-2)=ab^{-2}). Substitute (a = 21b^{4.5}) into (f(-2)), we have (f(-2)=21b^{4.5}\times b^{-2}=21b^{2.5}). Since (b^{5}=\frac{82}{21}), then (b^{2.5}=\sqrt{b^{5}}=\sqrt{\frac{82}{21}}). So (f(-2)=21\times\sqrt{\frac{82}{21}}).

[ \begin{align*} f(-2)&=\sqrt{21\times82}\ &=\sqrt{1722}\ &\approx41.5 \end{align*} ]

Answer:

(41.5)