Question

Item 2

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y=25(1.2)t. Evaluate the function when t=5. Round your answer to the nearest tenth.

Answer 1

The exponential function is y = 25(1.2)^t, with an initial amount a of 25 and a growth rate r of 20%. To find the value of y when t=5, raise 1.2 to the power of 5, multiply by 25, resulting in approximately 62.2.

Step-by-step explanation:

The exponential function given is y = 25(1.2)^t. Here, the initial amount a is 25 since that's the value of the function when t=0. The rate of growth r can be determined by converting the base of the exponential part of the function, 1.2, into a percent. The base 1.2 indicates a 20% growth rate because 1.2 is equivalent to 100% initial plus 20% growth. To evaluate the function when t=5, we simply substitute 5 for t:

y = 25(1.2)^5

Calculating the expression (1.2)^5 and then multiplying it by 25 gives us the value of y:

y = 25 × (2.48832)

y ≈ 62.2

Therefore, when t=5, the value of y is approximately 62.2 (rounded to the nearest tenth).