Determining exponential growth and decay in exercise, use the given information to write an exponential equation for y. does the function represent exponential growth or exponential decay?
dy/dt = 5.2y, y = 18 when t = 0

Exponential growth

Step-by-step explanation:

We can solve this differential equation by the separation of variables method.

We have that:

So

Integrating both sides

In which K is the value of y when t = 0.

We apply the exponential to both sides, so:

This is our exponential equation. Since the power of e is a positive value, the function represents exponential growth.

3.4 yards cubed, after rounding.

Step-by-step explanation:

To find the volume of a rectangular prism, use the following formula:

, where w is the width, l is the length, and h is the height

Substitute the values given to you into the formula:

Simplify the mixed number by multiplying both the numerator and denominator of 2/1 by 5 to get 10/5 and add it to the fraction to get 14/5.

Now, multiply the numerators and denominators of the fractions and simplify:

The volume is 3.36 yards cubed. Round to the nearest tenth to get 3.4 yards cubed.