Initial Amount: 350 Rate of Growth: 75 % Value When t=5: ≈ 5744.6
Practice makes perfect
Let's start by recalling the general formulas for exponential growth and exponential decay functions.
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Exponential Growth & Exponential Decay [0.8em]
y=a(1+r)^t & y=a(1-r)^t
In both cases a>0 is the initial amount and r>0 is the rate of growth or decay written in decimal form. Moreover, for exponential decay r is less than 1.
y= 350(1+ 0.75)^t
Our function represents exponential growth, with an initial amount a= 350 and a rate of growth r= 0.75. To rewrite the rate of growth as a percent, we move the decimal point two places to the right.
r=0.75 ⇔ r=75 %
Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula.
<deduct>
y=350(1+0.75)^t
Add terms
y=350(1.75)^t
t= 5
y=350(1.75)^{{\color{#0000FF}{5}}}
expand Evaluate right-hand side
Calculate power
y=350(16.413085\ldots)
Multiply
dnapxe
y=5744.580078\ldots
Round to 1 decimal place(s)
y\approx 5744.6
</deduct>
