The average rate of change in a function from a to b is
.
For the left function, from x = 4 to x = 5, the rate of change is
.
For the right function, the rate of change is
Using a ratio to compare the right function's growth rate with that of the left function, you get .
The right function is growing approximately 21 times faster than the left function (over the interval from 4 to 5).
The function the represent the balance in the account as a function of time t is p(t) = 1000 + 40t
<h3><u>Solution:</u></h3>Given that,
Carmen deposits $1000 into simple interest account
The rate for the account is 4%
To find: function the represent the balance in the account as a function of time t
Given is simple interest account
The formula for simple interest is given as:
Where, "p" is the principal and "r" is the rate of interest and "t" is the number of years
In simple interest,
total amount after "t" years = principal + simple interest
Here in this question, Carmen deposits $1000
Thus we can frame a function as:
total amount after "t" years = principal + simple interest
Where, p(t) is the amount after "t" years and is the principal sum
Thus the function is obtained