Question

A quantity with an initial value of 450 grows exponentially at a rate of 0.4% every 10

years. What is the value of the quantity after 96 years, to the nearest hundredth?

Answer 1

467.58

Explanation:

Grows 0.4% --> r = .004

Grows every 10 years: exponent of t/10

where t is in years

Write a function:

f(t) = 450(1+0.004)^t/10

96 years means no time conversion is needed due to years being the only unit in the problem

T = 96

f(96) = 450(1+0.004)^96/10

= 467.580247756

≈467.58

youre welcome y'all

Answer 2

The value of the quantity after 96 years is approximately 504 to the nearest hundredth.

To find the value of the quantity after 96 years, use the formula for exponential growth A = P × (1 + r)^t/n. Plugging in the values from the question, the value is approximately 504.

To find the value of the quantity after 96 years, we can use the formula for exponential growth: A = P × (1 + r)t/n. Here, A is the final value, P is the initial value, r is the growth rate per time period, t is the total time, and n is the number of time periods.

Plugging in the values from the question, we have A = 450 × (1 + 0.004)^9.6.

Evaluating this expression, we get A = 503.99 ≈ 504