Respuesta :
Answer:
t=4.3
Step-by-step explanation:
y=a(2)^{\frac{t}{d}}
y=a(2)
d
t
y=6800\hspace{40px}a=5500\hspace{40px}d=14
y=6800a=5500d=14
d is the doubling time
\text{Plug in:}
Plug in:
6800=
6800=
\,\,5500(2)^{\frac{t}{14}}
5500(2)
14
t
\text{Solve for }t\text{:}
Solve for t:
\frac{6800}{5500}=
5500
6800
=
\,\,\frac{5500(2)^{\frac{t}{14}}}{5500}
5500
5500(2)
14
t
Divide by 5500
1.23636364=
1.23636364=
\,\,2^{\frac{t}{14}}
2
14
t
\log(1.23636364)=
log(1.23636364)=
\,\,\log\left(2^{\color{green}{\frac{t}{14}}}\right)
log(2
14
t
)
Take the log of both sides
\log(1.23636364)=
log(1.23636364)=
\,\,\color{green}{\frac{t}{14}}\log(2)
14
t
log(2)
Bring exponent to the front
\frac{\log(1.23636364)}{\log(2)}=
log(2)
log(1.23636364)
=
\,\,\frac{t}{14}
14
t
Divide by log(2)
0.30610313=
0.30610313=
\,\,\frac{t}{14}
14
t
Divide in calculator
14(0.30610313)=
14(0.30610313)=
Multiply by 14
4.285443788=
4.285443788=
\,\,t
t
