Question

The price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $3?

P(t) = 1.1 e0.047t

Answer 1

do you mean
\[P(t)=1.1e^{0.047t}\]
or
\[P(t)=1.1\times e \times 0.047t\]

Answer 2

the first one sorry

Answer 3

Ahh, I thought so
Anyways you are given
\[P(t)=3\]
Therefore
\[1.1e^{0.047t}=3\]
\[e^{0.047t}=\frac{3}{1.1}\]
Now, do you know how to solve after this for t?

Answer 4

Not really :(

Answer 5

I would divide 3 by 11

Answer 6

Have you not read about logarithms?

Answer 7

I have but I'm having hard time understanding it

Answer 8

Ok, at this point you'd have to take log to the base e(also known as the natural log or just ln for short) on both sides of equation

Answer 9

ok

Answer 10

Here are some rules,
\[\log_{e}(e^x)=\ln(e^x)=x \]
\[\log _{e}\frac{a}{b}=\ln\frac{a}{b}=\log_{e}(a)-\log_{e}(b)=\ln(a)-\ln(b)\]
try using these rules to solve that equation, let me know if you have any problems

Answer 11

Ok, Thank you

Answer 12

\[\log_{e}(e)=1\]
and
\[\log_{e}(e^x)=xlog_{e}(e)=x\]

Answer 13

the answer I got was 21.35...

Answer 14

let me check

Answer 15

\[T = \ln (3/1.1)/0.047\]

Answer 16

Yeah, seems to be correct

Answer 17

Excellent, Indeed
\[t=\ln (\frac{3}{1.1})\frac{1}{0.047}\]

Answer 18

\[t=\frac{\ln(3)-\ln(1.1)}{0.047}\]

Answer 19

I have serious trouble with word problems :(

Answer 20

If you don't have a calculator or you are not allowed, you'd have to convert that to base 10
\[\log_{10}\] the standard logarithm and look up the values from a log table

Answer 21

Thank you for helping me

Answer 22

remember this formula
\[\log_{e}(x)=2.303\log_{10}(x)\]

Answer 23

In general,
\[\log_{b}(x)=\frac{\log_{a}(x)}{\log_{a}(b)}\]
\[\frac{1}{\log_{10}(e)}=2.303\]

Answer 24

Ok

Answer 25

\[\log_{e}(x)=\frac{\log_{10}(x)}{\log_{10}(e)}=\frac{1}{\log_{10}(e)} \times \log_{10}(x)=2.303\log_{10}(x)\]

Answer 26

can anyone help me. i have a ques to ask. but the ques requires a lot of drawings so thats y it can be posted on openstudy. tell me ur gmail adress and i will email the ques to u and then u can help me. please its midnight in my country and tommorow i have to submit the homework. in my country if u dont do the homework then u get a lot of beatings from the teacher. even i will get beatings. please help me i beg u. i fall on ur feet. i will never forget ur he;p in my life