Answer:
Step-by-step explanation:
We want to write an exponential function that goes through the points (0, 20) and (6, 1280).
The standard exponential function is given by:
The point (0, 20) tells us that <em>y</em> = 20 when <em>x</em> = 0. Hence:
Simplify:
So, our exponential function is now:
Next, the point (6, 1280) tells us that <em>y</em> = 1280 when <em>x</em> = 6. Thus:
Solve for <em>b</em>. Divide both sides by 20:
Therefore:
Hence, our function is:
Answer:
The function is y = 40 * 2^(x/2)
The graph is in the image attached
Step-by-step explanation:
The function that models this growth is an exponencial function, that can be described with the following equation:
y = a * b^(x/n)
Where a is the inicial value, b is the rate of growth, x is the time and n is the relation between the time and the rate (the rate occurs for every two hours, so n = 2).
Then, using a = 40, r = 2 and n = 2, we have:
y = 40 * 2^(x/2)
If we plot this function, we have the graph shown in the image attached,
It is an exponencial graph, where the value of y increases very fast in relation to the increase of x.
First, you need to find where you can move the decimal point to so that there is only one non-zero digit to the left of it.
Move the decimal point, and that is the first part done.
Add "".
For the last part - the power, you need to find how many decimal places you moved the decimal point. In this case, we moved it to the right 2 places, so the power is .
If, for example, we had moved the decimal point three places to the left, the power would be .