Answer :
Answer:
Step-by-step explanation:
Exponential functions have the standard form
[tex]y=a(b)^x[/tex]
where a is the initial value and b is the growth/decay rate. The rule is that the function is growth if the value for b is greater than 1; the function is decay if the value for b is greater than 0 but less than 1. Our b value is 1.5, so this is a growth function.
The tricky part about the growth rate is determining what the percent increase is. When you are dealing with a growth rate, you start with 100% of what you're dealing with, and are then adding to it the growth rate. For example, if the initial population of bacteria in a dish is 10 and it increases at a rate of 5% per hour, then the rate of increase in the function would be the 100% of the population that we started with plus 5%, giving us a growth rate of 100% + 5% = 105%. In decimal form that would be 1.05.
For us in our problem, we have the 100% of whatever to start with and added another 50% to that to give us a growth rate of 150%, or in decimal form, 1.5. So the increase is 50%
Given function is a growth function and the percentage rate of increase is 50%.
Given function in the question,
- [tex]y=740(1.5)^x[/tex]
If a function is given by,
[tex]y=I(1+\frac{r}{100})^x[/tex]
y = Final value
I = Initial value
r = rate of increase or decrease
x = Duration
If 'r' is positive, function will be a growth function and for negative value of 'r', function will be a decay function.
Given function 'y' can be written as,
[tex]y=740(1+\frac{50}{100} )^x[/tex]
Since, rate is positive, given function will be a growth function.
And the rate of increase will be r = 50%
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