Respuesta :
Answer:
Evaluate f(7)
[tex] f(7) = 240(0.7)^7 = 19.765[/tex]
Determine x when f(×)=120
[tex] 120 = 240 (0.7)^x[/tex]
We can derive both sides by 240 and we got:
[tex] 0.5 = 0.7^x[/tex]
Now we can apply natural log on both sides and we got:
[tex] ln(0.5)= x ln(0.7)[/tex]
And if we solve for the value of x we got:
[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]
And then the value of x = 1.943
Step-by-step explanation:
We have the following function given:
[tex]f(x) = 240(0.7)^x [/tex]
Evaluate f(7)
And we want to find [tex] f(7) [/tex] so we just need to replace x=7 and we got:
[tex] f(7) = 240(0.7)^7 = 19.765[/tex]
Determine x when f(×)=120
And for the second part we want to find a value of x who satisfy that the function would be equal to 120 and we can set up this:
[tex] 120 = 240 (0.7)^x[/tex]
We can derive both sides by 240 and we got:
[tex] 0.5 = 0.7^x[/tex]
Now we can apply natural log on both sides and we got:
[tex] ln(0.5)= x ln(0.7)[/tex]
And if we solve for the value of x we got:
[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]
And then the value of x = 1.943
