Every year, a town surveys the size of its wetland ecosystems. This equation estimates the total wetland area, in acres, over time, t, in years. F(t)= 740(0.95)^t

Which statements are supported by the function?

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

When t=10, the town is predicted to have around 492 acres of wetlands.

The wetland area in the town increases by 95% per year.

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Given

Required

The true statements

We have:

Substitute 10 for t

Hence, (a) is true

We have:

Substitute 740 for f(t)

Divide through by 740

Express 1 as 0.95^0

Cancel out the bases

Hence, the area had 740 acres initially;

(b) is true

We have:

Using the general formula

By comparison:

0.95 < 1 means that:

--- where r = rates

Collect like terms

Express as percentage

Hence, (c) is true

In (a)

Hence, (d) is false

In (c)

---- decrement

Hence, (e) is incorrect

f

step-by-step explanation:

f