Question

In 2010, Cornfield Farms produced 175,000 bushels of corn. Each year since 2010, their total corn harvest has increased by 2.5% over the previous year.

Write an exponential function, f(x), that models the number of bushels of corn produced x years after 2010.

Enter your answer by filling in the boxes.

f(x)= · ( )x

Answer 1

Answer:

f(x)=(2.5)x

Step-by-step explanation:

x equals the number of years after 2010, and every year after 2010 their total corn harvest increases by 2.5%, so you would have 2.5 multiplied by however many years after 2010 it is

Answer 2

The exponential function f(x) that models the number of bushels of corn produced x years after 2010 is f(x) = 175000(1.025)^x

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

We can use compound interest formula whenever there is compounding (increment or decrement) per unit time.

Here, the initial amount of  production farm was doing in 2010 is 175000 bushels of corn.

This value increases by 2.5% per year.

We need the final number of bushels of corn that will be produce x years after 2010.

So, here, we can take P = 175000, R = 2.5, and T = x

Then, we get:

$f(x) = A = 175000\left(1 + \dfrac{2.5}{100}\right)^x\\\\f(x) = 175000(1.025)^x$

Thus, the exponential function f(x) that models the number of bushels of corn produced x years after 2010 is $f(x) = 175000(1.025)^x$

Learn more about compound interest here:

https://brainly.com/question/11897800