The half-life of the given exponential function is of 346.57 years.
<h3>What is the half-life of an exponential function?</h3>
It is the value of t when A(t) = 0.5A(0).
In this problem, the equation is:
.
In which t is measured in years.
Hence the half-life is found as follows:
![0.5A(0) = A(0)e^{-0.002t}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29e%5E%7B-0.002t%7D)
![e^{-0.002t} = 0.5](https://tex.z-dn.net/?f=e%5E%7B-0.002t%7D%20%3D%200.5)
![\ln{e^{-0.002t}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.002t%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![0.002t = -\ln{0.5}](https://tex.z-dn.net/?f=0.002t%20%3D%20-%5Cln%7B0.5%7D)
![t = -\frac{\ln{0.5}}{0.002}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B0.002%7D)
t = 346.57 years.
More can be learned about exponential functions at brainly.com/question/25537936
#SPJ1
Answer:
Im not rally sure but maybe 5.71 , here is my explanation :
Step-by-step explanation:
Tan 55 =x/4
tan 55 = 1/42814
1/42814 = x /4
×=5.712592027 .
Y=mx+b is the slope formula
6/5 because flip the second number and multiply when dividing fractions.
A)
D+Y=50
D=Y+10
b)
Y+10+Y=50
2Y+10=50
2Y=40
Y=20
Therefore there are 20 in yearbook and 30 in drama.
To check our work:
D=Y+10
30=20+10
30=30 [CHECKS TRUE]