Question 1194927
<br>
{{{f(x)=ba^(-x)+c}}}<br>
(1) For large values of x, a^(-x) goes to zero, so the function is {{{f(x)=c}}}.  The value of the function approaches 350 for very large values of x, so c=350.  The function is<br>
{{{f(x)=ba^(-x)+350}}}<br>
(2) When x=0, a^(-x)=1, so the function is {{{f(x)=b+350}}}.  Since f(0)=70,<br>
{{{b+350=70}}}
{{{b=-280}}}<br>
The function is<br>
{{{f(x)=-280a^(-x)+350}}}<br>
(3) The function value is 300 when x=10.<br>
{{{300=-280a^(-10)+350}}}
{{{280a^(-10)=50}}}
{{{a^(-10)=50/280=5/28}}}
{{{a^10=28/5=5.6}}}
{{{a=5.6^(1/10)}}} = 1.18800 to 5 decimal places.<br>
ANSWER: The function is<br>
{{{f(x)=-280(1.188)^(-x)+350}}}<br>