Question

a quantity with an initial value of 5900 decays exponentially at a rate of 0.85% every 7 years. what is the value of the quantity after 99 months, to the nearest hundredth?

Answer 1

The value of the quantity after 99 months is 5228.58.

Given that,  an initial value = 5900, rate of decay = 0.85% and time period = 7 years.

What is the exponential decay?

The quantity decreases slowly after which the rate of change and the rate of growth decreases over a period of time rapidly. This decrease in growth is calculated by using the exponential decay formula.

The exponential decay formula formula is $Amount=Initial\ value(1-\frac{r}{100} )^{\frac{t}{n} }$

Here, the value $=5900(1-\frac{0.85}{100} )^{\frac{99}{7} }$

= 5900×$(0.9915)^{14.14}$

= 5900×0.8862

= 5228.58

Therefore, the value of the quantity after 99 months is 5228.58.

Learn more about the exponential decay here:

brainly.com/question/13674608.

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