Thread: Exponential and logarithmic

hey, i haven't been for quite a while

1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.

2. How would you go about sketching 2* 10^(x/10)+4?

3. y=2^x, y=3^x and y= 5^x
i. For what of value of x is 2^x > 3^x > 5^x
ii. For what value of x is 2^x < 3^x < 5^x
iii. For what value of x is 2^x = 3^x = 5^x

Thanks

Originally Posted by chaneliman

hey, i haven't been for quite a while

1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.

2. How would you go about sketching 2* 10^(x/10)+4?

3. y=2^x, y=3^x and y= 5^x
i. For what of value of x is 2^x > 3^x > 5^x
ii. For what value of x is 2^x < 3^x < 5^x
iii. For what value of x is 2^x = 3^x = 5^x

Thanks

to #1:

Solve for x:

(I've got 35 days)

to #2:

with

to # 3(iii):



(i) x < 0
(ii) x > 0

Originally Posted by chaneliman

hey, i haven't been for quite a while

1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.

is roughly 35, in other words, 35 days.

Originally Posted by chaneliman

2. How would you go about sketching 2* 10^(x/10)+4?

You are supposed to already know the basic form of an exponential curve.

Let x = 0
Then you will find y = 6

So you know it intersects the y-axis at 6

We can make infinitely small, but not exactly zero.

So if that part is infinitely small, we have on constant (+ 4) which will be our asymptote. See the attached image for clarification.

Originally Posted by chaneliman

3. y=2^x, y=3^x and y= 5^x
i. For what of value of x is 2^x > 3^x > 5^x
ii. For what value of x is 2^x < 3^x < 5^x
iii. For what value of x is 2^x = 3^x = 5^x

i) Where x < 0
ii) Where x > 0
iii) Where x = 0