Need help with 2 college algebra questions

[JackieG]

Problems
If you start a biology experiment with 5,000,000 cells and 45% of the cells are dying every minute, how long will it take to have less than 1000 cells? Start by constructing a model of the form A=A(knot)e^kt, then use it to answer the question.

If you put aside 1 cent on the first day, 2 cents on the second day, 4 cents on the third day, and so forth (doubling the amount each day) the model A(t)=2^t-1 can be used to determine the total of money put aside after t days. How many days will it take before you become a millionaire?

I am unsure how to set these up to solve them. Can you please help me.

thanks
Jackie

 

[HallsofIvy]

Problems
If you start a biology experiment with 5,000,000 cells and 45% of the cells are dying every minute, how long will it take to have less than 1000 cells? Start by constructing a model of the form A=A(knot)e^kt, then use it to answer the question.

If you put aside 1 cent on the first day, 2 cents on the second day, 4 cents on the third day, and so forth (doubling the amount each day) the model A(t)=2^t-1 can be used to determine the total of money put aside after t days. How many days will it take before you become a millionaire?

I am unsure how to set these up to solve them. Can you please help me.

thanks
Jackie

You are told that A= A_0 e^{kt}, that when t= 0 seconds, A_0e^0= A_0= 5000000 and that t= 0, A_0e^k(1)= A_0e^k= .45(5000000) so you can find both A_0 and k. Once you know those, set A= A_0e^{kt}= 1000 and solve for t.

If you Have A(t)= 2^(t- 1) (NOT (2^t)- 1) in pennies, then you need to solve 2^(t- 1)= 100000000.

I assume, since you are given this problem, you know that you can solve A^x= B by taking a logarithm of both sides.

 

[JackieG]

Help

So problem 1 my problem would look like

A=5,000,000_o e^(2,250,000)(1) ???

I did not understand what you were saying with problem 2.

I have A=1,000,000 and t is what I am solving for right?

So my problem would be 1,000,000(x)=2(t-1) ???