# Thread: College Algebra help: exponential and logarithmic Functions

1. ## College Algebra help: exponential and logarithmic Functions

The population of the world was 3 billlion in 1960 and it increased on average at annual of 18%...
In what year does the world population reach 5 billion ppl.

2. Originally Posted by Peyton Sawyer
The population of the world was 3 billlion in 1960 and it increased on average at annual of 18%...
In what year does the world population reach 5 billion ppl.
Year 0: $\displaystyle P = 3\cdot 10^9$

Year 1: $\displaystyle P = 1.18\cdot 3 \cdot 10^9$

Year 2: $\displaystyle P = 1.18\cdot 1.18 \cdot 3 \cdot 10^9$

Year 3: $\displaystyle P = 1.18 \cdot 1.18 \cdot 1.18 \cdot 3 \cdot 10^9$.

Can you see that the equation for Year $\displaystyle n$ would be

$\displaystyle P = 3\cdot 10^9 \cdot 1.18^n$.

Now let $\displaystyle P = 5 \cdot 10^9$ and solve for $\displaystyle n$.

3. Originally Posted by Prove It
Year 0: $\displaystyle P = 3\cdot 10^9$

Year 1: $\displaystyle P = 1.18\cdot 3 \cdot 10^9$

Year 2: $\displaystyle P = 1.18\cdot 1.18 \cdot 3 \cdot 10^9$

Year 3: $\displaystyle P = 1.18 \cdot 1.18 \cdot 1.18 \cdot 3 \cdot 10^9$.

Can you see that the equation for Year $\displaystyle n$ would be

$\displaystyle P = 3\cdot 10^9 \cdot 1.18^n$.

Now let $\displaystyle P = 5 \cdot 10^9$ and solve for $\displaystyle n$.
Determine how long it takes for an investment to double its value if the interest rate is 7% compounded continuously. Show equation set up.

4. Originally Posted by Peyton Sawyer
Determine how long it takes for an investment to double its value if the interest rate is 7% compounded continuously. Show equation set up.

Also, did you manage to finish the last question?

5. Originally Posted by Prove It

Also, did you manage to finish the last question?
its part B to the first question.
And im still working on finishing it up. its sort of difficult

6. For the first question:

$\displaystyle 5\cdot 10^9 = 3\cdot 10^9 \cdot 1.18^n$

$\displaystyle 1.18^n = \frac{5}{3}$

$\displaystyle \left(\frac{59}{50}\right)^n = \frac{5}{3}$

$\displaystyle \ln{\left(\frac{59}{50}\right)^n} = \ln{\frac{5}{3}}$

$\displaystyle n\ln{\frac{59}{50}} = \ln{\frac{5}{3}}$

$\displaystyle n = \frac{\ln{\frac{5}{3}}}{\ln{\frac{59}{50}}}$

$\displaystyle = \frac{\ln{5} - \ln{3}}{\ln{59} - \ln{50}}$.

$\displaystyle A = Pe^{rt}$.
Here $\displaystyle A = 2P, r = \frac{7}{100}$.
Solve for $\displaystyle t$.