Answer:
[tex]1.76[/tex] days
Step-by-step explanation:
**Note this propably is not what you are looking for but it gets you the final answer.**
Given the eqaution [tex]y=9^{5x}[/tex]
Lets solve for x.
Step 1.
Rewirte the equation as [tex]y=a^{bx}[/tex]. Where [tex]a=9[/tex] and [tex]b=5[/tex].
Step 2.
Take the natural logarithm of both sides. Then rewrite the left hand side using properties of exponents/logarithms.
[tex]ln(y)=b*x*ln(a)[/tex]
Step 3.
Divide both sides of the equation by [tex]b[/tex]
[tex]\frac{ln(y)}{b} =x*ln(a)[/tex]
Step 4.
Divide both sides of the equation by [tex]ln(a)[/tex]
[tex]\frac{ln(y)}{b*ln(a)} =x[/tex]
Now we have our equation to solve for the number of days.
Step 5.
Plug [tex]9[/tex] back in for [tex]a[/tex] and [tex]5[/tex] back in for [tex]b[/tex].
[tex]\frac{ln(y)}{5*ln(9)} =x[/tex]
Step 6.
We are given 243 million for [tex]y[/tex].
Lets plug in 243 million.
[tex]\frac{ln(243,000,000)}{5*ln(9)} =x[/tex]
Step 7.
Solve for x.
[tex]x=1.7575419...[/tex]
Lets round to the hundreth's place.
[tex]x=1.76[/tex]
1.76 days
