Mathematics: 1950, the u.s. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. find an exponential function to model this data

A.Step-by-step explanation:Formula for Circumference isWe know radius is half of diameter...

1950, the u.s. federal budget was $39.4 billion, - id1950394219510, destineecoleman2001

taquanhamilton68

10.03.2022

Let's do the usual thing and make t the years since 1950. We'll just abbreviate a billion B.

f(1950-1950)=39.4 B

f(2000-1950) =2025.2 B

Our exponential form for f will be

$f = a e^{kt}$

$39.4 \textrm{ B} = a e^{ 0 k} = a$

$2025.2 \textrm{ B} = a e^{50 k}$

Dividing

$\dfrac{2025.2}{39.4} = e^{50 k}$

$50 k = \ln \dfrac{2025.2}{39.4}$

$k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932$

Our function is

$f = 39.4 \textrm{ B } e^{0.0787932 t }$

Since $e^{0.0787932} \approx 1.08198$

$f = 39.4 \textrm{B } 1.08198^t }$

around 8.2 % annualized growth.

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leannaadrian

13.01.2023

$C= 28.3 \ \ feet$

Step-by-step explanation:

Formula for Circumference is

$C=2\pi r$

We know radius is half of diameter

$r=\frac{d}{2} \\r=\frac{9}{2}$

$C=2(3.14)\frac{9}{2}$

$C=(3.14)9\\C=28.3 feet$

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