Question

The air in a cheap football given by the formula f (x) = 100 * 0.997 ^ { x} where x is the number of days since the ball has been pumped and f ( x) are measured as a percentage of what a fullpumpad ball normally should be.
a) Calculate and interpret f ( 7).
Can u help me plz
After how many days remain only 75% of the air? Calculate exactly and then round off the whole day .

Answer 1

Hello,

a)
$f(7)=100*0.997^{7}=97.91880558....$

b)
$f(x)=100*0.997^{x}= \dfrac{3}{4}\\ ==\ \textgreater \ \ 0.997^x= \dfrac{3}{400} \\ ==\ \textgreater \ \ x\ ln(0.997)=ln( \dfrac{3}{400})\\\\ ==\ \textgreater \ \ x=1628.503100163296....$≈1629 (days)