Q: What is the equation of the exponential curve that passes through the points (0,3) and (5, 96)?
Answer: y=3 (2)x
10 months. First you subtract what is already in possession from what they need: $1450-$1200= $250 Then you would divide how much money is left to earn by how much money is gained every year: $250 divided by $25= 10 months Hope this helps!!
I know that just the answer is not enough. You need to understand why and how. So I will explaing the steps.
First you need to state the equation that represents the function.
Investment is $200 and interest rate is 5%, y is the amount of money after x periods.
Note that after 1 period the amount of money is 200 plus 5% interest, which is 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)
After 2 periods the amount is 200(1.05)*(1.05) = 200 (1.05)^2
After 3 periods the amount is 200 (1.05)^3
And now you can deduce that after x periods y = 200 (1.05)^x
You can then analyze the function to predict the shape and critical points of the graph.
The answers are based in the initial value and the increasing factor.
The initial value is when x = 0, which yields to y = 200 (1.05)^0 = 200*1 = 200
And the increasing factor is 1.05 because any value is the previos one times 1.05.
Then the answer is the first option. The initial value is 200 and the graph increases by a factor of 1.05 per 1 unit increase in time.
