Question

Amy had a beautiful plant. The plant began sprouting two days before Amy bought it, and she had it for 98 days before it died. At its tallest, the plant was 30 centimeters tall. Let h(t) denote the height of Amy's plant h (measured in centimeters), t days from the time she bought it. Define the Domain in interval notation.

Answer 1

The Domain interval notation is -2 < t < 98

Explanation:

The given parameters are;

The time at which the plant began spouting = 2 days before Amy bought it

The number of days the plant was with Amy = 98 days

The maximum height reached by the plant = 30 centimetres

Given that the height of the plant is represented by the function h(t), where h is in centimetres and t is the number of days from the time she bought the plant

Therefore, we have;

At t = -2, h = 0

At t = 98, h = 30

The slope of the function is therefore;

m = (30 - 0)/(98 - (-2)) = 0.3 cm/day

The equation of the function is therefore;

h - 30 = 0.3 × (t - 98)

h = 0.3·t -29.4 + 30 = 0.3·t + 0.6

h(t) = 0.3·t + 0.6

At h(t) = 0, t = -2

At h(t) = 30, t = 98

The interval notation of the domain is therefore, -2 < t < 98.